Results 11 to 20 of about 136,858 (207)
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. We also show that a strongly pseudoconvex complex Finsler manifold with semi-positive but not identically zero holomorphic sectional ...
Wan X.
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Four-manifolds of Pinched Sectional Curvature
Pacific Journal of Mathematics, 2019 In this paper, we study closed four-dimensional manifolds. In particular, we show that under various new pinching curvature conditions (for example, the sectional curvature is no more than 5/6 of the smallest Ricci eigenvalue) then the manifold is ...
Cao, Xiaodong, Tran, Hung
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Sectional curvature and Weitzenbock formulae
Indiana University Mathematics Journal, 2022 We establish a new algebraic characterization of sectional curvature bounds $\sec\geq k$ and $\sec\leq k$ using only curvature terms in the Weitzenböck formulae for symmetric $p$-tensors. By introducing a symmetric analogue of the Kulkarni-Nomizu product, we provide a simple formula for such curvature terms.
Bettiol, R., Mendes, R.
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Sweeping out sectional curvature [PDF]
Geometry & Topology, 2014 We observe that the maximal open set of constant curvature k in a Riemannian manifold with curvature bounded below or above by k has a convexity type property, which we call "two-convexity". This statement is used to prove a number of rigidity statements in comparison geometry.
Panov, D., Petrunin, A.
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Positive weighted sectional curvature [PDF]
Indiana University Mathematics Journal, 2017 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
Kennard, Lee, Wylie, William
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Strongly positive curvature [PDF]
, 2014 We begin a systematic study of a curvature condition (strongly positive curvature) which lies strictly between positive curvature operator and positive sectional curvature, and stems from the work of Thorpe in the 1970s.
Bettiol, Renato G. +1 more
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On the scalar curvature and sectional curvatures of a Kaehler submanifold [PDF]
Proceedings of the American Mathematical Society, 1973 For a Kaehler submanifold of a complex space form, pinching for scalar curvature implies pinching for sectional curvatures. 1 . Statement of result. The scalar curvature is, by definition, the sum of Ricci curvatures with respect to an orthonormal basis of the tangent space, and the Ricci curvature is the sum of sectional curvatures.
Chen, Bang-Yen, Ogiue, Koichi
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Chern-Ricci curvatures, holomorphic sectional curvature and Hermitian metrics [PDF]
Science China Mathematics, 2019 19 ...
Chen, Haojie +2 more
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Positive biorthogonal curvature on S^2 x S^2
, 2013 We prove that S^2 x S^2 satisfies an intermediate condition between having metrics with positive Ricci and positive sectional curvature. Namely, there exist metrics for which the average of the sectional curvatures of any two planes tangent at the same ...
Bettiol, Renato G.
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A sectional curvature for statistical structures
, 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.Comment: 19 ...
Opozda, Barbara
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