Results 1 to 10 of about 1,739,776 (377)
On the sectional curvature of lightlike submanifolds [PDF]
Journal of Inequalities and Applications, 2016 The main purpose of this paper is to show how to obtain rigidity theorems with the help of curvature invariants in submanifolds of a semi-Riemannian manifold.
Erol Kılıç, Mehmet Gülbahar
doaj +4 more sources
Curvature Invariants of Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature [PDF]
Entropy, 2018 In this article, we consider statistical submanifolds of Kenmotsu statistical manifolds of constant ϕ-sectional curvature. For such submanifold, we investigate curvature properties. We establish some inequalities involving the normalized δ-Casorati
Simona Decu +3 more
doaj +3 more sources
Chern-Ricci curvatures, holomorphic sectional curvature and Hermitian metrics [PDF]
arXiv, 2019 We present some formulae related to the Chern-Ricci curvatures and scalar curvatures of special Hermitian metrics. We prove that a compact locally conformal K\"{a}hler manifold with constant nonpositive holomorphic sectional curvature is K\"{a}hler.
Xiaolan Nie, Lingling Chen, Haojie Chen
arxiv +6 more sources
On the boundary behavior of the holomorphic sectional curvature of the Bergman metric [PDF]
arXiv, 2006 We obtain a conceptually new differential geometric proof of P.F. Klembeck's result that the holomorphic sectional curvature of a strictly pseudoconvex domain approaches (in the boundary limit) the constant sectional curvature of the Bergman metric of the unit ball.
Barletta, Elisabetta
arxiv +8 more sources
On the Sectional Curvature of Compact Hypersurfaces [PDF]
Proceedings of the American Mathematical Society, 1990 We establish a sufficient condition for compact hypersurfaces of a complete riemannian manifold to be spherical. It is well known, from the works of Jacobowitz, Jorge and Koutroufiotis, and others, that the maximum sectional curvature of such hypersurfaces can be estimated from the curvature of the ambient space and the outer radius.
Leslie Coghlan, Yoe Itokawa
openalex +3 more sources
A conclusive theorem on Finsler metrics of sectional flag curvature [PDF]
arXiv, 2018 If the flag curvature of a Finsler manifold reduces to sectional curvature, then locally either the Finsler metric is Riemannian, or the flag curvature is isotropic.
Huang, Libing, Shen, Zhongmin
arxiv +3 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
openalex +3 more sources
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
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