The study characterizes spacetimes with quasi-constant sectional curvature and explores their properties in F(R)-gravity.
problem Characterizing spacetimes with quasi-constant sectional curvature.
method Investigation through examples, proofs, and analysis of energy conditions.
result A spacetime of quasi-constant sectional curvature can represent a Robertson Walker spacetime or a static spacetime.
The aim of this paper is to describe Kahler surfaces with quasi-constant holomorphic curvature
The aim of this paper is to classify compact Kahler manifolds with quasi-constant holomorphic sectional curvature.
The Kaehler manifolds of quasi-constant holomorphic sectional curvatures are introduced as Kaehler manifolds with complex distribution of codimension two, whose holomorphic sectional curvature only depends on the corresponding point and the geometric angle, associated with the section. A curvature identity characterizi…
We prove that closed manifolds admitting a generic metric whose sectional curvature is locally quasi-constant are graphs of space forms. In the more general setting of QC spaces where sets of isotropic points are arbitrary, under suitable positivity assumption and for torsion-free fundamental groups they are still diff…
The Eisenhart problem of finding parallel tensors treated already in the framework of quasi-constant curvature manifolds in \cite{x:j} is reconsidered for the symmetric case and the result is interpreted in terms of Ricci solitons. If the generator of the manifold provides a Ricci soliton then this is i) expanding on p…
Study on generalized quasi-Einstein structures in contact geometry.
problem Characterizing and understanding generalized quasi-Einstein structures in contact geometry.
method Investigation of properties, existence, and characterizations of generalized quasi-Einstein normal metric contact pair manifolds.
result Normal metric contact pair manifolds with generalized quasi-constant curvature are generalized quasi-Einstein manifolds.
Riemannian manifolds of quasi-constant sectional curvatures (QC-manifolds) are divided into two basic classes: with positive or negative horizontal sectional curvatures. We prove that the Riemannian QC-manifolds with positive horizontal sectional curvatures are locally equivalent to canal hypersurfaces in Euclidean spa…
The study shows that certain manifolds are conformally flat and have a specific equation of state.
problem Characterizing properties of extended recurrent pseudo-Riemannian manifolds.
method Reconsideration and analysis of Mileva Prvanovic's work, showing conformal flatness and quasi-constant curvature.
result Extended recurrent Lorentzian manifolds with time-like associated covector are perfect fluid Robertson-Walker spaces with a specific equation of state.
In this paper, we show that a generalized Sasakian space form of dimension greater than three is either of constant sectional curvature; or a canal hypersurface in Euclidean or Minkowski spaces; or locally a certain type of twisted product of a real line and a flat almost Hermitian manifold; or locally a wapred product…
We prove that every Kaehler metric, whose potential is a function of the time-like distance in the flat Kaehler-Lorentz space, is of quasi-constant holomorphic sectional curvatures, satisfying certain conditions. This gives a local classification of the Kaehler manifolds with the above mentioned metrics. New examples o…
Using as an underlying manifold an alpha-Sasakian manifold we introduce warped product Kaehler manifolds. We prove that if the underlying manifold is an alpha-Sasakian space form, then the corresponding Kaehler manifold is of quasi-constant holomorphic sectional curvatures with special distribution. Conversely, we prov…
The paper describes a specific type of Kähler surfaces.
problem Understanding QCH Kähler surfaces with quasi-constant holomorphic sectional curvature.
method Detailed description of generalized Calabi type QCH Kähler surfaces.
result Detailed description of QCH Kähler surfaces of generalized Calabi type.
The paper introduces comprehensive quasi-Einstein spacetimes and explores their properties.
problem Exploring new types of spacetimes in general relativity.
method Mathematical analysis of geometric and physical properties of comprehensive quasi-Einstein manifolds.
result Existence of comprehensive quasi-Einstein spacetimes and their properties.
The study improves Wintgen inequalities for submanifolds in specific geometric spaces.
problem Improving Wintgen inequalities for submanifolds in various geometric spaces.
method Analyzing submanifolds in conformally flat manifolds and deriving inequalities for different types of spaces.
result Derived inequalities for submanifolds in various geometric spaces, including Riemannian manifolds of quasi-constant curvature and warped products.
Study finds conditions for certain warped product manifolds to be quasi-Einstein.
problem Conditions for quasi-Einstein sequential warped product manifolds.
method Investigated necessary and sufficient conditions for specific types of manifolds.
result Identified conditions for sequential warped product manifolds to be quasi-Einstein.
Study curves' intersections and distances, with applications in graph and group studies.
problem Understanding intersections and distances of curves.
method Using a relationship between intersection numbers and subsurface projection distances, applications in curve graphs and mapping class groups.
result Explicit quasi-constants for the relationship between intersection numbers and subsurface projection distances.
We study different notions of Riemannian curvatures: The p-curvatures which interpolate between the scalar curvature and the sectional curvature, the Gauss-Bonnet-Weyl curvatures form another interpolation from the scalar curvature to the Gauss-Bonnet integrand. We bring out the (p,q)-curvatures, which incorporate …
Paper establishes a relation between Berwald scalar curvature and S-curvature.
problem Understanding the relationship between Finsler metrics' curvature properties.
method Proved conditions for isotropic Berwald scalar curvature and weakly isotropic S-curvature.
result Finsler metrics with isotropic Berwald scalar curvature have weakly isotropic S-curvature.
New scalar curvature defined from Ollivier-Ricci curvature for graphs.
problem Defining scalar curvature for graphs and point clouds.
method Defining a new scalar version of Ollivier-Ricci curvature and proving its convergence.
result The new scalar curvature converges to scalar curvature for sampled manifolds.
The paper examines complete Yamabe solitons with finite total scalar curvature.
problem Characterizing complete Yamabe solitons with specific curvature properties.
method Analyzing steady or shrinking complete gradient Yamabe solitons with finite total scalar curvature and non-positive Ricci curvature.
result Steady or shrinking complete gradient Yamabe solitons with finite total scalar curvature and non-positive scalar curvature have zero scalar curvature.
We show any Riemannian curvature model can be geometrically realized by a manifold with constant scalar curvature. We also show that any pseudo-Hermitian curvature model, para-Hermitian curvature model, hyper-pseudo-Hermitian curvature model, or hyper-para-Hermitian curvature model can be realized by a manifold with co…
Study on Hermitian metrics and curvature properties of complex manifolds.
problem Analyzing curvature properties of Hermitian metrics on complex manifolds.
method Derivation of formulae and proofs for Chern-Ricci curvatures and holomorphic sectional curvatures.
result Examples of metrics with specific curvature properties.
The paper studies special Finsler spaces with Hp-scalar curvature.
problem Characterizing and investigating Finsler spaces with specific scalar curvatures.
method Intrinsic investigation and various conditions for transformations between Finsler spaces.
result Conditions for transforming Finsler spaces of scalar curvature to those of Hp-scalar curvature. Paper explores entropic curvature in Markov chains, comparing it to other curvatures.
problem Comparing entropic curvature to other curvatures in Markov chains.
method Adapted Γ-calculus for θ-curvatures, explicit lower bounds, curvature perturbation.
result Entropic curvature differs significantly from other curvature notions.
New metric with negative curvature found near positive-curvature spaces.
problem Understanding spaces with positive curvature bounds.
method Analyzing metrics in relation to curvature bounds.
result Near any point in a positive-curvature space, there exists a metric with negative upper curvature.
Study examines preservation of curvature-adaptedness during mean curvature flow.
problem Preservation of curvature-adaptedness during mean curvature flow.
method Investigates curvature-adaptedness in locally symmetric spaces.
result Curvature-adaptedness is preserved along mean curvature flow.
The paper studies Finsler manifolds with a new curvature concept.
problem Understanding Finsler manifolds with positive weighted flag curvature.
method Introducing a new curvature concept based on the flag curvature and a non-Riemannian quantity, T-curvature.
result Positive weighted flag curvature implies the manifold is diffeomorphic to Euclidean space.
The paper studies Berwald scalar curvature properties in Finsler geometry.
problem Characterizing Finsler manifolds based on Berwald scalar curvature.
method Analyzes properties of Berwald scalar curvature and its implications for Finsler manifolds.
result Landsberg manifolds with vanishing Berwald scalar curvature are Berwald manifolds.
New proof shows holomorphic sectional curvature fully determines curvature tensor.
problem Determining the curvature tensor from holomorphic sectional curvature.
method Representation-theoretic means to calculate L2-norm of holomorphic sectional curvature. result Holomorphic sectional curvature fully determines the curvature tensor.
Study rigidity of Einstein metrics as critical points of curvature functionals.
problem Characterize Einstein metrics as critical points of quadratic curvature functionals.
method Analyze pointwise inequalities involving Weyl curvature and traceless Ricci curvature.
result Provide rigidity results for Einstein metrics and locally conformally flat critical metrics.
Given a compact four dimensional smooth Riemannian manifold (M,g) with smooth boundary, we consider the evolution equation by Q-curvature in the interior keeping the T-curvature and the mean curvature to be zero and the evolution equation by T-curvature at the boundary with the condition that the Q-curvature …
The study classifies critical metrics on manifolds with specific curvature conditions.
problem Characterizing critical metrics for quadratic curvature functionals.
method Analyzing closed n-dimensional manifolds with Ricci, scalar curvature, and Riemannian curvature tensor.
result Critical metrics are Einstein under certain curvature conditions.
The curvature-dimension condition implies a new weighted scalar curvature.
problem Studying the properties of the n-volumic scalar curvature. method Using the curvature-dimension condition mCD(κ,n) and smGH-convergence. result The stability of n-volumic scalar curvature ≥κ under smGH-convergence. Rigidity results for manifolds with positive scalar curvature under curvature inequalities.
problem Understanding rigidity properties of manifolds with positive scalar curvature.
method Proving rigidity under specific curvature inequalities involving Weyl curvature, traceless Ricci curvature, and Yamabe invariant.
result Rigidity results for Bach-flat closed manifolds and 4-dimensional manifolds.
Compact shrinkers with curvature pinching conditions proven.
problem Ensuring shrinkers are compact under curvature pinching conditions.
method Various curvature pinching conditions applied to shrinkers with positive Ricci curvature and asymptotically nonnegative sectional curvature.
result Shrinkers with curvature pinching conditions are proven to be compact.
Estimates curvature and radius for constant mean curvature surfaces.
problem Understanding the geometry of surfaces with constant mean curvature.
method Intrinsic curvature and radius estimates for compact disks, applied to complete surfaces.
result Global geometry of constant mean curvature surfaces studied.
Study pinches intrinsic and normal curvatures of minimal surfaces in a sphere.
problem Pinching constraints on intrinsic and normal curvatures of minimal surfaces.
method Established orthonormal frame field, derived property K+KN=1, used to pinch curvatures. result Pinched constraints on intrinsic and normal curvatures of minimal surfaces.
Study geodesic curvature of logarithmic spirals on curved surfaces.
problem Understanding geodesic curvature on curved surfaces.
method Computed geodesic curvature of logarithmic spirals on surfaces of constant Gaussian curvature.
result Asymptotic behavior of geodesic curvature is independent of the ambient surface's curvature.
Extending results about positive scalar curvature to non-negative curvature.
problem Extending results about positive scalar curvature to non-negative curvature.
method Using index theory to generalize results.
result Explicit generalizations of classical results about positive scalar curvature metrics to non-negative curvature metrics.
New curvature definitions for networks simplify complex computations.
problem Complex curvature calculations for networks.
method Introducing new curvature definitions based on Menger and Haantjes curvatures.
result Simplified and faster computation of network curvatures.
Study on singularity behavior of mean curvature flow with bounded curvature and index.
problem Understanding singularity formation in mean curvature flow with constraints.
method Analyzing flow with bounded mean curvature and Morse index.
result Either mean curvature or Morse index blows up at first singular time.
Study on curvature in finitely generated groups, showing positive curvature in specific cases.
problem Understanding curvature in finitely generated groups.
method Analyzing dead-end elements and related elements to find curvature, studying effect of radius.
result Examples of positive curvature for arbitrary radius in lamplighter and Houghton's group.
Introduces new curvature concept for Kähler manifolds.
problem Optimizing curvature constraints for projective Kähler manifolds.
method Introduces weighted orthogonal Ricci curvature and proves vanishing theorems.
result Proves optimal curvature constraints for projective Kähler manifolds.
The study sets limits on scalar curvature in positive curvature manifolds.
problem Bounding scalar curvature in positive curvature manifolds.
method Establishing inequalities for manifolds with positive scalar curvature and scalar curvature bounded from below.
result Established inequalities for manifolds with positive scalar curvature.
The paper studies Kropina metrics with a specific curvature property.
problem Characterizing Kropina metrics with isotropic scalar curvature.
method Tensor analysis to derive expressions and characterize metrics.
result Characterization of Kropina metrics with isotropic scalar curvature.
We introduce a natural extension of the metric tensor and the Hodge star operator to the algebra of double forms to study some aspects of the structure of this algebra. These properties are then used to study new Riemannian curvature invariants, called the (p,q)-curvatures. They are a generalization of the p-curvat…
Proves curvature estimates for 3D surfaces solving scalar curvature equations.
problem Estimating curvature of 3D surfaces solving scalar curvature equations.
method Integral method and new Lagrangian submanifold observation.
result Interior curvature estimates for 3D hypersurfaces are proven.