The paper examines curvature properties of twistor spaces.
problem None explicitly stated in the abstract.
method Review of Riemannian and almost Hermitian geometry of twistor spaces.
result Curvature properties of twistor spaces are explored.
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48 results for “Riemannian properties”
Proves properties of sub-Riemannian exponential map, showing it's not injective.
problem Regularity and continuity of sub-Riemannian exponential map.
method Used sub-Riemannian Jacobi fields and Maslov index of Jacobi curves.
result Exponential map of 3D Heisenberg group is not injective near conjugate vectors.
Study properties of specific submanifolds in metallic Riemannian spaces.
problem Characterize warped product pointwise bi-slant submanifolds.
method Analyze in locally metallic Riemannian manifolds with examples in Euclidean spaces.
result Construct examples of warped product pointwise bi-slant submanifolds.
In this article we study the validity of the Whitney extension property for horizontal curves in sub-Riemannian manifolds endowed with 1-jets that satisfy a first-order Taylor expansion compatibility condition. We first consider the equiregular case, where we show that the extension property holds true whenever a…
The aim of our paper is to focus on some properties of submanifolds in Riemannian manifolds endowed with endomorphisms that generalize the Golden Riemannian structure, named metallic Riemannian structures. We focus on the properties of the structure induced on submanifolds, named by us -metallic Riemannian structure…
The main aim of the present work is to obtain some curvature properties of the manifolds from two classes of Riemannian product manifolds. These classes are two basic classes from Naveira classification of Riemannian almost product manifolds.
Study expands classical harmonic function results to Riemannian manifolds.
problem Classical harmonic function properties in domains of Riemannian manifolds.
method Generalized classical results to Riemannian manifolds, including pinched negative curvature.
result Generalized results for Riemannian manifolds, including pinched negative curvature.
Geodesic orbit pseudo-Riemannian H-type nilmanifolds: case of minimal admissible Clifford modulesmath.DG
Study geodesic orbit property on pseudo-Riemannian H-type nilmanifolds.
problem Characterize geodesic orbit property for pseudo-Riemannian H-type Lie groups.
method Extend results from Riemannian to pseudo-Riemannian H-type Lie groups, focusing on minimal admissible Clifford modules.
result Complete characterization of geodesic orbit property for pseudo-Riemannian H-type Lie groups.
The study examines properties of biharmonic hypersurfaces with torse-forming vector fields.
problem Properties of biharmonic hypersurfaces in Riemannian manifolds.
method Investigates biharmonic hypersurfaces with torse-forming vector fields.
result Provides properties of biharmonic hypersurfaces with torse-forming vector fields.
We study compact Riemannian manifolds for which the light between any pair of points is blocked by finitely many point shades. Compact flat Riemannian manifolds are known to have this finite blocking property. We conjecture that amongst compact Riemannian manifolds this finite blocking property characterizes the flat m…
The study of spectral-tightness in Riemannian manifolds and its topological implications.
problem Understanding the spectral properties of Riemannian manifolds and their coverings.
method Analyzing the fundamental group and the Euclidean local de Rham factor to characterize spectral-tightness.
result Spectral-tightness is a topological property of the fundamental group, and it can be characterized by the dimension of the Euclidean local de Rham factor.
We build an analogue for the Levi-Civita connection on Riemannian manifolds for sub-Riemannian manfiolds modeled on the Heisenberg group. We demonstrate some geometric properties of this connection to justify our choice and show that this connection is unique in having these properties.
Study on properties of tangential hypersurfaces in product-like manifolds.
problem Investigating properties of tangential hypersurfaces in product-like manifolds.
method Analyzing basic properties and computing curvature tensor relations.
result Computed relations involving the Riemannian curvature tensor of tangential hypersurfaces.
Paper proves naturally reductive property is inaudible for certain manifolds.
problem Proving naturally reductive property is inaudible for specific manifolds.
method Using a pair of non-compact 11-dimensional generalized Heisenberg groups, the paper proves the naturally reductive property is inaudible.
result The naturally reductive property is inaudible for certain manifolds.
Every convex set in a generic Riemannian manifold has peculiar properties.
problem Characterizing convex sets in Riemannian manifolds.
method Analyzing geodesics and hypersurfaces in Riemannian manifolds.
result Convex sets in generic Riemannian manifolds are strictly convex if bounded by smooth hypersurfaces.
Heat flow fails to preserve concavity in curved spaces.
problem Non-preservation of concavity properties in curved spaces.
method Analysis of Dirichlet heat flow on Riemannian manifolds.
result No concavity properties are preserved unless curvature is zero.
Extends p-harmonic map theory for new properties.
problem No specific problem stated; extends existing theory.
method Extended p-harmonic and biharmonic map definitions.
result New properties of generalized stable p-harmonic maps.
Study para-Ricci-like solitons on special Riemannian manifolds, proving geometric properties and providing an example.
problem Characterize para-Ricci-like solitons on para-Sasaki-like Riemannian -manifolds.
method Analyzed different cases of potential vectors and proved geometric properties of constructed objects.
result Obtained results for a parallel symmetric second-order covariant tensor and provided an explicit example.
Failure of the measure contraction property via quotients in higher-step sub-Riemannian structuresmath.DG
New sub-Riemannian structures fail synthetic curvature bounds.
problem Failure of synthetic curvature bounds in sub-Riemannian geometry.
method New stability results for local MCP under quotients, applied to specific sub-Riemannian structures.
result Ideal sub-Riemannian structures can fail the MCP, generically for high dimensions and rank > 3.
Study on pseudo-Riemannian Bertrand manifolds finds no closed movement systems.
problem Exploring properties of pseudo-Riemannian Bertrand manifolds.
method Proof of properties and discussion of the theory.
result No pseudo-Riemannian completely Bertrand systems exist.
Conformal Riemannian P-Manifolds with Connections whose Curvature Tensors are Riemannian P-Tensorsmath.DG
The largest class of Riemannian almost product manifolds, which is closed with respect to the group of the conformal transformations of the Riemannian metric, is the class of the conformal Riemannian P-manifolds. This class is an analogue of the class of the conformal Kähler manifolds in almost Hermitian geometry. The …
The study classifies quasi-minimal surfaces in 4D pseudo-Riemannian space-forms with positive nullity.
problem Characterizing surfaces in pseudo-Riemannian space forms with positive nullity.
method Analyzing the relative null space and classifying quasi-minimal surfaces.
result Classifications of quasi-minimal surfaces with positive relative nullity.
Study on null helices in semi-Riemannian manifolds with special submanifolds.
problem Investigating geometric properties of null helices on totally umbilical submanifolds in 3D semi-Riemannian manifolds.
method Using the null Frenet frame and degenerate metric condition, equations and invariants characterizing null helices are derived.
result Equations and invariants characterizing null helices on totally umbilical submanifolds in 3D semi-Riemannian manifolds are obtained.
We prove that two-step analytic sub-Riemannian structures on a compact analytic manifold equipped with a smooth measure and Lipschitz Carnot groups satisfy measure contraction properties.
Study curvature properties of specific Riemannian manifolds with skew-circulant structures.
problem Investigate curvature of Riemannian manifolds with a particular tensor structure.
method Analyze 4D Riemannian manifolds with right skew-circulant tensor S, invariant under S and g, focusing on Ricci tensor and sectional curvatures.
result Obtained properties of curvature tensors and sectional curvatures for specific manifolds.
Study on Riemannian properties of SU_n using bi-invariant metric.
problem Properties of SU_n with a specific bi-invariant metric.
method Analyzes distance, diameter, and geodesics in SU_n.
result Parametrizes minimizing geodesic segments using a complex Grassmannian.
New insights into manifold properties using Seiberg-Witten and harmonic theories.
problem Characterizing properties of 4-manifolds with specific geometric conditions.
method Combining Seiberg-Witten theory on compact manifolds and harmonic theory on non-compact manifolds, with a new argument for asymptotic properties.
result Found a pair of homeomorphic 4-manifolds with distinct geometric properties under Riemannian metrics.
We give asymptotically tight estimates of tangent space variation on Riemannian submanifolds of Euclidean space with respect to the local feature size of the submanifolds. We show that the result follows directly from structural properties of local feature size of the Riemannian submanifold and some elementary Euclidea…
Top dimensional group of the basic intersection cohomology for singular riemannian foliationsmath.DG
It is known that, for a regular riemannian foliation on a compact manifold, the properties of its basic cohomology (non-vanishing of the top-dimensional group and Poincaré Duality) and the tautness of the foliation are closely related. If we consider singular riemannian foliations, there is little or no relation betwee…
New method for modeling densities on Riemannian manifolds with symmetries.
problem Modeling densities on Riemannian manifolds with known symmetry groups.
method Combining implicit neural layers and optimal transport theory to propose IRCPMs.
result IRCPMs are simpler to incorporate symmetries and less expensive than ODE-flows.
New examples of hyperbolic Riemannian manifolds proven.
problem Understanding hyperbolic Riemannian manifolds.
method Proving an analogue of the Brody lemma and presenting new examples.
result New examples of Kobayashi hyperbolic Riemannian manifolds.
Classification of biharmonic Riemannian submersions from manifolds with constant sectional curvaturemath.DG
This paper generalizes biharmonic Riemannian submersions to higher dimensions.
problem Classifying biharmonic Riemannian submersions from manifolds with constant sectional curvature.
method Constructing an adapted orthonormal frame to simplify the biharmonic equation and analyzing curvature properties.
result A Riemannian submersion is biharmonic if and only if it is harmonic from an -dimensional manifold with constant sectional curvature to an -dimensional manifold.
We study metric contraction properties for metric spaces associated with left-invariant sub-Riemannian metrics on Carnot groups. We show that ideal sub-Riemannian structures on Carnot groups satisfy such properties and give a lower bound of possible curvature exponents in terms of the datas.
Rigging technique introduced in \cite{bi0} is a convenient way to address the study of null hypersurfaces. It offers in addition the extra benefit of inducing a Riemannian structure on the null hypersurface which is used to study geometric and topological properties on it. In this paper we develop this technique showin…
Study on spectral properties of Riemannian submersions with special fibers.
problem Analyzing spectral properties of Riemannian submersions with fibers of basic mean curvature.
method Comparing the spectrum of the total space with a Schrödinger operator on the base manifold, extending results on Riemannian coverings.
result Computed the bottom of the spectrum and Cheeger constant for connected, amenable Lie groups.
By a classical result of Darboux, a foliation of a Riemannian surface has the Graves property (also known as the strong evolution property) if and only if the foliation comes from a Liouville net. A similar result of Blaschke says that a pair of orthogonal foliations has the Ivory property if and only if they form a Li…
Geodesic orbit property studied for Lorentz manifolds.
problem Geodesic orbit property for Lorentz manifolds.
method Defined naturally reductive for pseudo-Riemannian manifolds and proved theorems for Lorentz nilmanifolds.
result Geodesic orbit property holds for Lorentz nilmanifolds under specific conditions.
New Dynkin condition for manifolds with boundary yields bi-Lipschitz equivalence and spectral properties.
problem Characterizing smooth Riemannian manifolds with boundary.
method Introducing a Dynkin-type condition and proving its equivalence to a weighted manifold.
result Bi-Lipschitz equivalence and various spectral properties of manifolds with boundary.
Study properties of semi-symmetric Lorentzian spaces, foliated manifolds.
problem Properties of semi-symmetric pseudo-Riemannian manifolds.
method Investigate foliated manifolds with Lorentzian metrics and analyze Ricci operator eigenvalues.
result Ricci operator has only real eigenvalues for Lorentzian metrics.
Establishes a concavity property for positive Hessian quotient operators.
problem Analyzing positive Hessian quotient operators on Riemannian manifolds.
method Proves a special concavity property and a Jacobi inequality.
result Proves a Jacobi inequality for symmetric tensors.
The authors define a SNS (semi-nearly-sub)-Riemannian connection on nearly sub-Riemannian manifolds and study the geometric properties of such a connection, and obtain the natures of horizontal curvature tensors between horizontal sub-Riemannian connection and SNS-Riemannian connection. The authors further investigate …
We introduce length dilatation structures on metric spaces, tempered dilatation structures and coherent projections and explore the relations between these objects and the Radon-Nikodym property and Gamma-convergence of length functionals. Then we show that the main properties of sub-riemannian spaces can be obtained f…
Final part of a series on nonlinear observers on Riemannian metrics, establishing conditions for convergence.
problem Ensuring convergence of nonlinear observers on Riemannian metrics.
method Analyzing the nullity of the second fundamental form of the output function and its relationship to the infinite gain margin property.
result Formulated sufficient and necessary conditions for the nullity of the second fundamental form, linking it to the infinite gain margin property.
Study proves estimate for Hessian quotient equations on 2D Riemannian manifolds.
problem Problems posed by Delanoë and Urbas related to Hessian quotient equations.
method Maximum principle argument and new test function introduced to prove estimate.
result Unobstructed second order a priori estimate for real Hessian quotient equation in 2D.
Let be an n-dimensional Riemannian manifold and be its cotangent bundle equipped with a Riemannian metric of Cheeger Gromoll type which rescale the horizontal part by a nonzero differentiable function. The main purpose of the present paper is to discuss curvature properties of and construct al…
In this paper, using connections between Clifford-Wolf isometries and Killing vector fields of constant length on a given Riemannian manifold, we classify simply connected Clifford-Wolf homogeneous Riemannian manifolds. We also get the classification of complete simply connected Riemannian manifolds with the Killing pr…
We study the six-dimensional pseudo-Riemannian spaces with two time-like coordinates that admit non-homothetic infinitesimal projective transformations. The metrics are manifestly obtained and the projective group properties are determined. We also find a generic defining of projective motion in the 6-dimensional rigid…
The paper proves Weyl projective rigidity for sub-Riemannian metrics and shows genericity of such metrics.
problem Investigating the Weyl projective rigidity of sub-Riemannian metrics.
method Analytic and smooth category proofs for specific distributions with minimal order complex abnormal extremals.
result Genericity of Weyl projectively rigid sub-Riemannian metrics and distributions.