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Some Inequalities on Sectional Curvature
, 2010
"... Abstract The aim of this paper is to study some inequalities relating the sectional curvatures of indefinite totally real submanifolds with the corresponding curvature of the indefinite complex space form and the size of the second fundamental form of the submanifold. Mathematics Subject Classifica ..."
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Abstract The aim of this paper is to study some inequalities relating the sectional curvatures of indefinite totally real submanifolds with the corresponding curvature of the indefinite complex space form and the size of the second fundamental form of the submanifold. Mathematics Subject
Ricci flow and nonnegativity of sectional curvature
 11 (2004), 883–904, MR2106247, Zbl pre02152382
"... Abstract. In this paper, we extend the general maximum principle in [NT3] to the time dependent Lichnerowicz heat equation on symmetric tensors coupled with the Ricci flow on complete Riemannian manifolds. As an application we exhibit complete Riemannian manifolds with bounded nonnegative sectional ..."
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Cited by 16 (5 self)
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curvature of dimension greater than three such that the Ricci flow does not preserve the nonnegativity of the sectional curvature, even though the nonnegativity of the sectional curvature was proved to be preserved by Hamilton in dimension three. This fact is proved through a general splitting theorem
NEGATIVE SECTIONAL CURVATURE AND THE PRODUCT COMPLEX STRUCTURE
, 2006
"... Negative sectional curvature and the product complex structure ..."
SectionalCurvature Preserving Skinning Surfaces
, 1995
"... : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 11. Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 22. A family of skinn ..."
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of skinning interpolants : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 63. Sectionalcurvature preserving (scp) skinning interpolants : : : : : : : : : : : : : : : : : 114. An automatic algorithm for constructing scp skinning interpolants : : : : : : : : : 195
An exotic sphere with positive sectional curvature
, 2008
"... During the 1950s, a famous theorem in geometry and some perplexing examples in topology were discovered that turned out to have unexpected connections. In geometry, the development was the Quarter Pinched Sphere Theorem. ([Berg1], [Kling], and [Rau]) Theorem (RauchBergerKlingenberg, 19521961) If ..."
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Cited by 32 (7 self)
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1961) If a simply connected, complete manifold has sectional curvature between 1/4 and 1, i.e., 1/4 < sec ≤ 1, then the manifold is homeomorphic to a sphere. The topological examples were [Miln] Theorem (Milnor, 1956) There are 7manifolds that are homeomorphic to, but not diffeomorphic to, the 7sphere
Manifolds of Constant JSectional Curvature
, 2009
"... The goal of this paper is to present EulerLagrange and Hamiltonian equations on which is a model of paraKählerian manifolds of constant Jsectional curvature. In conclusion, some differential geometrical and physical results on the related mechanic systems have been given. ..."
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The goal of this paper is to present EulerLagrange and Hamiltonian equations on which is a model of paraKählerian manifolds of constant Jsectional curvature. In conclusion, some differential geometrical and physical results on the related mechanic systems have been given.
SYMMETRIES OF SECTIONAL CURVATURE ON 3–MANIFOLDS
, 1992
"... Abstract In dimension three, there are only two signatures of metric tensors: Lorentzian and Riemannian. We find the possible pointwise symmetry groups of Lorentzian sectional curvatures considered as rational functions, and determine which can be realized on naturally reductive homogeneous spaces. ..."
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Abstract In dimension three, there are only two signatures of metric tensors: Lorentzian and Riemannian. We find the possible pointwise symmetry groups of Lorentzian sectional curvatures considered as rational functions, and determine which can be realized on naturally reductive homogeneous spaces
PARASASAKIAN MANIFOLDS WITH CONSTANT PARAHOLOMORPHIC SECTIONAL CURVATURE
, 2009
"... In this paper paraSasakian manifolds with constant paraholomorphic sectional curvature are considered. ..."
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In this paper paraSasakian manifolds with constant paraholomorphic sectional curvature are considered.
Examples of manifolds with nonnegative sectional curvature
, 2007
"... Manifolds with nonnegative sectional curvature have been of interest since the beginning of global Riemannian geometry, as illustrated by the theorems of BonnetMyers, Synge, and the sphere theorem. Some of the oldest conjectures in global Riemannian geometry, as for example the Hopf conjecture on ..."
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Cited by 10 (7 self)
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Manifolds with nonnegative sectional curvature have been of interest since the beginning of global Riemannian geometry, as illustrated by the theorems of BonnetMyers, Synge, and the sphere theorem. Some of the oldest conjectures in global Riemannian geometry, as for example the Hopf conjecture
Results 1  10
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1,706