Results 1 to 10 of about 1,771,677 (277)
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
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
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.
Haojie Chen, Lin Chen, Xiaolan Nie
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
Positive weighted sectional curvature [PDF]
arXiv, 2014 In this paper, we give a new generalization of positive sectional curvature called positive weighted sectional curvature. It depends on a choice of Riemannian metric and a smooth vector field. We give several simple examples of Riemannian metrics which do not have positive sectional curvature but support a vector field that gives them positive weighted
Lee Kennard, W. Wylie
arxiv +7 more sources
Holomorphic Sectional Curvature of Complex Finsler Manifolds. [PDF]
J Geom Anal, 2019 In this paper, we get an inequality in terms of holomorphic sectional curvature of complex Finsler metrics. As applications, we prove a Schwarz Lemma from a complete Riemannian manifold to a complex Finsler manifold.
Wan X.
europepmc +3 more sources
Sectional curvature and Weitzenbock formulae [PDF]
Indiana University Mathematics Journal, 2017 We establish a new algebraic characterization of sectional curvature bounds $\sec\geq k$ and $\sec\leq k$ using only curvature terms in the Weitzenbock formulae for symmetric $p$-tensors. By introducing a symmetric analogue of the Kulkarni-Nomizu product,
R. G. Bettiol, R. Mendes
semanticscholar +4 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
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
Sectional Curvature in Riemannian Manifolds
The Mathematica Journal, 2020 The metric structure on a Riemannian or pseudo-Riemannian manifold is entirely determined by its metric tensor, which has a matrix representation in any given chart.
B. Healy +2 more
semanticscholar +2 more sources