Generalized Roter type manifold is a generalization of conformally flat manifold as well as Roter type manifold, which gives rise the form of the curvature tensor in terms of algebraic combinations of the fundamental metric tensor and Ricci tensors upto level 2. The object of the present paper is to investigate the cha…
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48 results for “Roter type condition”
Geodesic mappings found in a specific type of warped product manifolds.
problem Characterizing geodesic mappings in a particular class of Roter spaces.
method Identifying a specific class of Roter type warped product manifolds and proving geodesic mappings onto another Roter type warped product manifold.
result Both geodesically related manifolds are pseudosymmetric of constant type.
The paper examines curvature properties of a specific magnetic spacetime metric.
problem Investigating the geometric properties of Melvin magnetic spacetime metric.
method Analyzing a Melvin type static, cylindrically symmetric spacetime metric in Weyl form, considering curvature conditions and tensor properties.
result The Melvin magnetic metric is pseudosymmetric and satisfies the Roter type condition.
The main object of the present paper is to study the geometric properties of a generalized Roter type semi-Riemannian manifold, which arose in the way of generalization to find the form of the Riemann-Christoffel curvature tensor . Again for a particular curvature restriction on and the Ricci tensor there ar…
Defines a new tensor related to special geometric spaces.
problem Understanding new curvature tensors in semi-Riemannian geometry.
method Defines a generalized curvature tensor using specific operations.
result The tensor is connected to quasi-Einstein, Roter, and Roter-type spaces.
On pseudosymmetric manifoldsmath.DG
In the literature, there are two different notions of pseudosymmetric manifolds, one by Chaki [7] and other by Deszcz [16], and there are many papers related to these notions. The object of the present paper is to deduce necessary and sufficient conditions for a Chaki pseudosymmetric [7] (resp. pseudo Ricci symmetric […
Study of hypersurfaces in curved spaces with specific curvature properties.
problem Characterizing hypersurfaces in spaces of constant curvature with particular curvature properties.
method Investigates hypersurfaces isometrically immersed in semi-Riemannian spaces of constant curvature, focusing on the curvature tensor and its properties.
result Hypersurfaces in the specified spaces satisfy a Roter type equation, linking their curvature tensor to specific tensor products.
The difference tensor C.R - R.C of Einstein manifolds, some quasi-Einstein manifolds and Roter type manifolds, of dimension n > 3, satisfy the following curvature condition: (A) C.R - R.C = Q(S,C) - (k /(n-1)) Q(g,C). We investigate hypersurfaces M in space forms N satisfying (A). The main result states that if the ten…
The curvature properties of Robinson-Trautman metric have been investigated. It is shown that Robinson-Trautman metric admits several kinds of pseudosymmetric type structures such as Weyl pseudosymmetric, Ricci pseudosymmetric, pseudosymmetric Weyl conformal curvature tensor etc. Also it is shown that the difference $R…
Som-Raychaudhuri spacetime is a stationary cylindrical symmetric solution of Einstein field equation corresponding to a charged dust distribution in rigid rotation. The main object of the present paper is to investigate the curvature restricted geometric structures admitting by the Som-Raychaudhuri spacetime and it is …
Investigates geometric properties of Bardeen black hole spacetime.
problem Examines curvature properties of Bardeen black hole spacetime.
method Analyzes pseudosymmetry, pseudosymmetric Weyl curvature, and recurrent structures.
result Bardeen spacetime is a manifold of pseudosymmetry Weyl curvature and satisfies special recurrent like structure.
Study explores geometric properties of Vaidya-Bonner-de Sitter spacetime.
problem Exploring geometric properties of Vaidya-Bonner-de Sitter spacetime.
method Analyzing conformal curvature, conharmonic curvature, and other curvatures.
result VBdS spacetime exhibits various pseudosymmetric structures and geometric features.
The paper examines geometric properties of a specific black hole spacetime.
problem Curvature properties of a Hayward black hole spacetime.
method Analyzes the curvature properties of Hayward black hole spacetime using Einstein field equations.
result The Hayward black hole spacetime is an Einstein manifold and exhibits various types of pseudosymmetry.
Compact ECS manifolds are proven to be bundles over the circle.
problem Compact ECS manifolds and their local structure.
method Proof of a specific result for compact rank-one ECS manifolds.
result Compact rank-one ECS manifolds, not locally homogeneous, are bundles over the circle.
Compact ECS manifolds have a simple topological structure.
problem Understanding the structure of compact ECS manifolds.
method Review of basic facts, construction of examples, and proof of a topological structure result.
result Compact rank-one ECS manifolds are bundles over S^1 with fibers being leaves of D⊥.
Lower bounds for eigenvalues on manifolds with boundary conditions.
problem Eigenvalue bounds for manifolds with boundary conditions.
method Proving lower bounds for the first non-trivial eigenvalue using Cheeger-type constants.
result Results in the spirit of Cheeger's inequality for manifolds with boundary conditions.
The paper studies Einstein-type manifolds with structural conditions.
problem Investigating geometric structures on Riemannian manifolds.
method Unified approach to various geometric structures and curvature conditions.
result Rigidity results for Einstein-type manifolds under specific curvature conditions.
Paper classifies Einstein-type manifolds with parallel Ricci tensor.
problem Classifying Einstein-type manifolds with specific curvature properties.
method Deduced Bochner-type identity and used it to show rigidity results.
result Found conditions for classifying Einstein-type manifolds with parallel Ricci tensor.
The paper finds sign-changing solutions for a specific type of elliptic equation.
problem Existence of sign-changing solutions for a Yamabe type equation.
method Investigates a critical elliptic equation with a Yamabe type operator on a compact manifold with boundary.
result Existence of sign-changing solutions assured under certain geometric conditions.
A Condition Ensuring Spatial Curves Develop Type-II Singularities Under Curve Shortening Flowmath.DG
We provide a condition for spatial curves which rules out the development of a type I singularity. The condition is that after the last time for which an inflection point develops, if the torsion is ever everywhere non-negative, the curve cannot develop a type I singularity.
The object of the present paper is to study the characterization of warped product manifolds satisfying some pseudosymmetric type conditions, especially, due to projective curvature tensor. For this purpose we consider a warped product manifold satisfying the pseudosymmetric type condition $R\cdot R = L_1 Q(g,R) + L_2 …
On the elliptic sinh-Gordon equation with integrable boundary conditions II -- Baker-Akhiezer theorymath.AP
Study finite-type solutions of elliptic sinh-Gordon equation with Durham boundary conditions.
problem Finite-type solutions of elliptic sinh-Gordon equation with Durham boundary conditions.
method Determine rationality criteria for Durham conditions and analyze spectral curve properties.
result Rationality criteria are sufficient for finite-type solutions with complementary boundary conditions.
New method uses CDMs to improve CI testing without distributional assumptions.
problem Testing conditional independence when the conditional distribution is unknown.
method Uses conditional diffusion models (CDMs) to approximate and a classifier-based CMI estimator.
result Proposed method performs better than GAN-based CI tests and controls type I and II errors.
Classifies Toda-type tt*-structures and their fixed points.
problem Classifying Toda-type tt*-structures and their fixed points.
method Fixed point description and reduction of anti-symmetry conditions.
result Reduces possibilities of anti-symmetry condition to two cases.
Let be a complete hyperbolic surface of infinite type with geodesic boundary which admits a countable pair of pants decomposition. As an application of the Basmajian identity for complete bordered hyperbolic surfaces of infinite type with limit sets of 1-dimensional measure zero, we define an asymmetric metric …
Study on self-similar sets on Riemannian manifolds with new separation conditions.
problem Analyzing self-similar sets on Riemannian manifolds with new separation conditions.
method Formulated weak separation and finite type conditions for conformal iterated function systems on Riemannian manifolds.
result Obtained formulas for Hausdorff dimensions of self-similar and graph self-similar sets.
Generalizes Ricci flow starting from small curvature concentration with a Morrey-type condition.
problem Ricci flow starting from manifolds with unbounded curvature.
method Replaces bounded curvature with a Morrey-type condition on the gradient of the metric relative to a complete bounded curvature metric.
result Long-time existence of Ricci flow with curvature decay estimates and diffeomorphic manifold.
Classifies local boundary conditions for Dirac-type operators on manifolds.
problem Determining all local smooth boundary conditions for Dirac-type operators.
method Combining general theory of boundary value problems for Dirac operators and pointwise considerations.
result Classification of local self-adjoint regular boundary conditions for Dirac spinors in dimensions 3 and 4.
We compute the index of a Callias-type operator with APS boundary condition on a manifold with compact boundary in terms of combination of indexes of induced operators on a compact hypersurface. Our result generalizes the classical Callias-type index theorem to manifolds with compact boundary.
Proves simple type conjecture for mod 2 Seiberg-Witten invariants.
problem Proving simple type conjecture for mod 2 Seiberg-Witten invariants.
method Analyzes cohomology ring conditions to prove simple type for all smooth structures.
result Shows existence of topological 4-manifolds with mod 2 simple type.
Paper generalizes ddc-condition to non-Kähler complex manifolds.
problem Characterizing complex manifolds beyond Kähler geometry.
method Introduces and studies a new ddc-type condition for complex manifolds.
result The new condition is open under deformations and applies to various manifolds.
Given a connected, compact, totally geodesic submanifold Y^m of noncompact type inside a compact locally symmetric space of noncompact type X^n, we provide a sufficient condition that ensures that [Y^m] is nonzero in H_m(X^n; R); in low dimensions, our condition is also necessary. We provide conditions under which ther…
The paper establishes gradient estimates for harmonic and heat equation solutions on manifolds with boundary.
problem Gradient estimates for harmonic and heat equation solutions on manifolds with boundary.
method Yau and Souplet-Zhang type gradient estimates for harmonic and heat equation solutions under Dirichlet boundary condition.
result Established gradient estimates for harmonic and heat equation solutions on manifolds with boundary.
Study rigidifies Einstein-type manifolds with boundary and constant curvature.
problem Classifying compact Einstein-type manifolds with boundary and constant scalar curvature.
method Applied recent results on gradient Einstein-type manifolds to prove rigidity.
result Rigidity results for compact Einstein-type manifolds with boundary and constant scalar curvature.
The paper improves eigenvalue estimates for manifolds with Ricci curvature conditions.
problem Eigenvalue estimates for manifolds with Ricci curvature conditions.
method Proves eigenvalue estimates using a Kato condition on the negative part of Ricci curvature.
result Optimal eigenvalue estimates for Zhong-Yang type and Cheng-type bounds.
Paper derives a Reilly type integral formula and applies it to inequalities and eigenvalue problems.
problem Developing a new integral formula and its applications in geometric inequalities and eigenvalue problems.
method Derives a Reilly type integral formula associated with the -Laplacian and applies it to inequalities and eigenvalue problems.
result Obtains Heintze-Karcher and Minkowski type inequalities, and eigenvalue relationships.
Proves conditions for Fourier transforms in rank 1 symmetric spaces.
problem Understanding Fourier transform bounds in symmetric spaces.
method Proves sufficient and necessary conditions using Lipschitz and Fourier type integral conditions.
result Establishes bounds for Fourier transforms in rank 1 symmetric spaces with specific moduli of continuity.
New inequalities for convex curves with multiple geometric factors.
problem Establishing inequalities for convex curves with multiple geometric factors.
method Parametric isoperimetric-type inequalities for closed convex curves with parameter conditions and equality conditions.
result Derived new inequalities and improved versions of existing inequalities.
Study short-time existence of Ricci-DeTurck flow from rough metrics with Morrey-type integrability.
problem Short-time existence of Ricci-DeTurck flow from rough metrics with specific integrability condition.
method Rough existence theory, preservation and improvement of scalar curvature bounds.
result Preservation and improvement of distributional scalar curvature lower bounds under certain conditions.
Topological structure of spaces of stability conditions and topological Fukaya type categoriesmath.RT
This is a survey on two closely related subjects. First, we review the study of topological structure of `finite type' components of spaces of Bridgeland's stability conditions on triangulated categories. The key is to understand Happel-Reiten-Smalo tilting as tiling of cells. Second, we review topological realizations…
Note on potential Kirby move type 1 for contact surgery diagrams.
problem Exploring conditions for a contact Kirby move type 1.
method Analyzing necessary conditions for contact surgery diagrams to be candidates for contact Kirby move type 1.
result Existence of a collection of contact positive integral surgery diagrams on Legendrian unknots satisfying the conditions.
Study proves conditions for Einstein-type manifolds with specific Weyl tensor properties.
problem Conditions for Einstein-type manifolds with specific Weyl tensor properties.
method Proved conditions for Einstein-type manifolds with fourth-order divergence-free Weyl tensor and zero radial Weyl curvature.
result Proved that a complete Einstein-type manifold with specific Weyl tensor properties is locally a warped product.
Paper shows how solutions to Allen-Cahn converge to multiphase mean curvature flow.
problem Convergence of Allen-Cahn solutions to multiphase mean curvature flow.
method Conditional convergence result of Allen-Cahn solutions to De Giorgi type BV-solutions of multiphase mean curvature flow.
result De Giorgi type BV-solutions are unique in a weak-strong sense.
In this paper, by a new method we establish the Weyl-type asymptotic formula for the counting function of biharmonic Stekloff eigenvalues with Neumann boundary condition in a bounded domain of an -dimensional Riemannian manifold.
We prove a Frobenius-type theorem for singular distributions generated by a family of locally Lipschitz continuous vector fields satisfying almost everywhere a quantitative finite type condition.
In this study, firstly, Mannheim curves with , are considered and the conditions are obtained for Mannheim curve to be slant helix. Moreover, the necessary and sufficient conditions are investigated for Mannheim curve to be AW(2), AW(3) and weak AW(2)-types, respectively. Lastly, it is sh…
The anomaly flow on a complex 3-fold is studied with integral Shi-type estimates and long-time existence conditions.
problem Long-time existence of the anomaly flow on a compact complex 3-fold.
method Integral Shi-type estimates adapted from integration-by-parts arguments, with a smallness condition on the slope parameter.
result Long-time existence of the anomaly flow on a compact complex 3-fold under a smallness condition on the slope parameter.
Ancient Ricci flows are identified without curvature sign condition.
problem Identifying type II ancient Ricci flows and their backward limits.
method Using a size condition of the sharp log Sobolev functional near infinity.
result Rigidity result for ancient Ricci flows without sign condition on curvatures.