Results 11 to 20 of about 1,771,776 (376)
Remarks on symplectic sectional curvature [PDF]
Differential Geometry and its Applications, 2016 In [11], I. M. Gelfand, V. Retakh, and M. Shubin defined the symplectic sectional curvature of a torsion-free connection preserving a symplectic form. The present article defines the corresponding notion of constant symplectic sectional curvature and characterizes this notion in terms of the curvature tensor of the symplectic connection and its ...
Daniel J. F. Fox
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On projectivized vector bundles and positive holomorphic sectional curvature [PDF]
, 2016 We generalize a construction of Hitchin to prove that, given any compact K\"ahler manifold $M$ with positive holomorphic sectional curvature and any holomorphic vector bundle $E$ over $M$, the projectivized vector bundle ${\mathbb P}(E)$ admits a K ...
Alvarez, Angelynn +2 more
core +2 more sources
Group-quotients with positive sectional curvatures [PDF]
Proceedings of the American Mathematical Society, 1977 Let H be a closed subgroup of compact Lie group G. A necessary and sufficient condition is obtained for the existence of a left-invariant Riemannian metric on G such that the subduced metric on the quotient H G has strictly positive sectional curvatures.
Robert Geroch
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Integrating holomorphic sectional curvatures [PDF]
arXiv, 2023 We calculate the $L^2$-norm of the holomorphic sectional curvature of a K\"ahler metric by representation-theoretic means. This yields a new proof that the holomorphic sectional curvature determines the whole curvature tensor. We then investigate what the holomorphic sectional curvature of a Hermitian metric determines and calculate the $L^2$-norm of ...
arxiv +3 more sources
A sectional curvature for statistical structures [PDF]
arXiv, 2015 A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.
B. Opozda
arxiv +3 more sources
SECTIONAL CURVATURES OF GRASSMANN MANIFOLDS [PDF]
Proceedings of the National Academy of Sciences, 1968 Yung-Chow Wong
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Mixed sectional-Ricci curvature obstructions on tori [PDF]
arXiv, 2017 We establish new obstruction results to the existence of Riemannian metrics on tori satisfying mixed bounds on both their sectional and Ricci curvatures. More precisely, from Lohkamp's theorem, every torus of dimension at least three admits Riemannian metrics with negative Ricci curvature. We show that the sectional curvature of these metrics cannot be
Kloeckner, Benoît, Sabourau, Stéphane
arxiv +2 more sources
Sectional curvature for Riemannian manifolds with density [PDF]
Geometriae Dedicata, 2013 In this paper we introduce two new notions of sectional curvature for Riemannian manifolds with density. Under both notions of curvature we classify the constant curvature manifolds. We also prove generalizations of the theorems of Cartan–Hadamard, Synge,
W. Wylie
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Developments around positive sectional curvature [PDF]
Surveys in Differential Geometry, 2009 This is not in any way meant to be a complete survey on positive curvature. Rather it is a short essay on the fascinating changes in the landscape surrounding positive curvature. In particular, details and many results and references are not included, and things are not presented in chronological order.
Karsten Grove
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On the higher order sectional curvatures [PDF]
Illinois Journal of Mathematics, 1975 A. M. Naveira
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