Results 171 to 180 of about 48,546 (184)

Scalar Curvature and Betti Numbers of Compact Riemannian Manifolds

Bulletin of the Brazilian Mathematical Society, New Series, 2019
For a compact oriented manifold \(M\) with positive scalar curvature, the author investigates the relationship between algebraic properties of the curvature tensor and the global geometry and topology of Riemannian manifolds (using Bachner technique in the context of manifolds with some type of curvature condition which implies that harmonic forms are ...
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The Sub-Riemannian Curvature of Contact Manifolds

This paper delves into the intricate concept of sub-Riemannian curvature within the framework of contact manifolds. Sub-Riemannian geometry, a generalization of Riemannian geometry where paths are constrained to a non-integrable distribution, presents unique challenges for defining curvature.
Revista, Zen, MATH, 10
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On Cohomogeneity Two Riemannian Manifolds of Non-Positive Curvature

Lobachevskii Journal of Mathematics, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the Pseudohermitian Curvature of Contact Semi-Riemannian Manifolds

Results in Mathematics, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Riemannian Manifolds of Positive Curvature

Proceedings of the International Congress of Mathematicians 2010 (ICM 2010), 2011
Simon Brendle, Richard Schoen
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Minimal Hypersurfaces in a Riemannian Manifold of Constant Curvature

American Journal of Mathematics, 1970
tures and n respectively, dim V1 = m> 1 and dim V2 =n-m ?1. Mr n-mn In the latter part of this statement, the second fundamental form A has two eigenvalues of multiplicities dim VI and dim V2. The main purpose of the present paper is to investigate the converse problem for minimal hypersurfaces in Sn+1.
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Hypersurfaces of a Riemannian manifold of constant curvature

2009
The theory of hypersurfaces, defined as submanifolds of codimension one, is one of the most fundamental theories of submanifolds. Therefore, in Sections 11–13 we consider hypersurfaces of a Riemannian manifold of constant curvature. This research, combined with the results obtained in Section 10, will contribute to studying real hypersurfaces of ...
Mirjana Djorić, Masafumi Okumura
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Evolution of hypersurfaces by their curvature in Riemannian manifolds

1998
The paper investigates some recent developments in the study of the motion of hypersurfaces in Riemannian manifolds when the normal speed is a monotonic function of the principal curvatures such that the evolution equation is a nonlinear parabolic PDE. In particular, the focus is on the mean curvature flow and, respectively, the inverse mean curvature ...
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Riemannian Curvature of a Manifold

2001
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Finiteness theorems for Riemannian manifolds of negative curvature

See the review in Zbl 0591.53039.
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