Results 11 to 20 of about 138,464 (231)
Sectional Curvature of Connections with Vectorial Torsion
Russian Mathematics, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
E D Rodionov
exaly +4 more sources
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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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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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.
Coghlan, Leslie, Itokawa, Yoe
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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
core +1 more source
The curvature of contact structure on 3-manifolds [PDF]
, 2008 We study the sectional curvature of plane distributions on 3-manifolds. We show that if the distribution is a contact structure it is easy to manipulate this curvature. As a corollary we obtain that for every transversally oriented contact structure on a
Candel +5 more
core +3 more sources
On the Sectional Curvature Along Central Configurations [PDF]
Regular and Chaotic Dynamics, 2018 14 pages, 4 ...
Jackman, Connor, Meléndez, Josué
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Four-manifolds of pinched sectional curvature
Pacific Journal of Mathematics, 2022 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 definite.
Cao, Xiaodong, Tran, Hung
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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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On Sectional Curvatures and Characteristic of Homogeneous Spaces [PDF]
Proceedings of the American Mathematical Society, 1966 where cn is the volume of the Euclidean unit n-sphere, Yn the nth sectional curvature (see the definition (2) below) and co the volume element of the Riemannian structure of X. It is a still open question, whether the fact that the usual sectional curvature (second order sectional curvature) 72 has a constant sign for all plane sections, has some ...
Greub, W., Tondeur, P.
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