Results 51 to 60 of about 2,699,199 (290)

The Gauss map of immersions of Riemannian manifolds in spaces of constant curvature

, 1968
With an immersion x of a Riemannian n-manifold M into a Euclidean Nspace E there is associated the Gauss map, which assigns to a point p of M the n-plane through the origin of E and parallel to the tangent plane of x(M) at x(p), and is a map of M into ...
M. Obata
semanticscholar   +1 more source

Finsler manifolds with Positive Weighted Flag Curvature [PDF]

arXiv, 2023
The flag curvature is a natural extension of the sectional curvature in Riemannian geometry. However there are many non-Riemannian quantities which interact the flag curvature. In this paper, we introduce a notion of weighted flag curvature by modifying the flag curvature with the non-Riemannian quantity, T-curvature. We show that a proper open forward
arxiv  

First Natural Connection on Riemannian Π-Manifolds

Mathematics, 2023
A natural connection with torsion is defined, and it is called the first natural connection on the Riemannian Π-manifold. Relations between the introduced connection and the Levi–Civita connection are obtained.
Hristo Manev
doaj   +1 more source

On isometric immersions of sub-Riemannian manifolds [PDF]

arXiv, 2022
We study curvature invariants of a sub-Riemannian manifold (i.e., a manifold with a Riemannian metric on a non-holonomic distribution) related to mutual curvature of several pairwise orthogonal subspaces of the distribution, and prove geometrical inequalities for a sub-Riemannian submanifold.
arxiv  

Riemannian Manifolds with Positive Sectional Curvature [PDF]

, 2014
This is a survey of recent results on manifolds with positive curvature from a series of lecture given in Guanajuato, Mexico in 2010. It also contains some hitsorical comments.
openaire   +2 more sources

Totally geodesic submanifolds of Riemannian manifolds and curvature-invariant subspaces

, 1996
An isometric immersion φ: S —» M of a Riemannian manifold S into another Riemannian manifold M is called totally geodesic if the geodesies in S are carried into geodesies in M. We call such a pair (S, φ) a totally geodesic submanifold of M. Nevertheless,
K. Tsukada
semanticscholar   +1 more source

Sharp Caffarelli–Kohn–Nirenberg inequalities on Riemannian manifolds: the influence of curvature [PDF]

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2017
We first establish a family of sharp Caffarelli–Kohn–Nirenberg type inequalities (shortly, sharp CKN inequalities) on the Euclidean spaces and then extend them to the setting of Cartan–Hadamard manifolds with the same best constant.
V. H. Nguyen
semanticscholar   +1 more source

Black Holes have Intrinsic Scalar Curvature

Reports in Advances of Physical Sciences, 2023
The scalar curvature R is invariant under isometric symmetries (distance invariance) associated with metric spaces. Gravitational Riemannian manifolds are metric spaces.
P. D. Morley
doaj   +1 more source

Curvature flows in semi-Riemannian manifolds [PDF]

Surveys in Differential Geometry, 2007
We prove that the limit hypersurfaces of converging curvature flows are stable, if the initial velocity has a weak sign, and give a survey of the existence and regularity results.
openaire   +3 more sources

Examples of Riemannian manifolds with positive curvature almost everywhere [PDF]

, 1999
We show that the unit tangent bundle of S 4 and a real cohomology CP 3 admit Riemannian metrics with positive sectional curvature almost everywhere. These are the only examples so far with positive curvature almost everywhere that are not also known to ...
P. Petersen, Frederick Wilhelm
semanticscholar   +1 more source