Results 1 to 10 of about 132,930 (155)
On the sectional curvature of compact hypersurfaces [PDF]
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
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A sectional curvature for statistical structures
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Opozda, Barbara
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Group-Quotients with Positive Sectional Curvatures [PDF]
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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SECTIONAL CURVATURES OF GRASSMANN MANIFOLDS [PDF]
Yung-Chow Wong
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Four-manifolds of pinched sectional curvature
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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On the higher order sectional curvatures [PDF]
A. M. Naveira
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On the scalar curvature and sectional curvatures of a Kaehler submanifold [PDF]
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.
Koichi Ogiue, Bang-yen Chen
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Sweeping out sectional curvature [PDF]
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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Sectional curvature and Weitzenbock formulae
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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Strongly positive curvature [PDF]
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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