Results 1 to 10 of about 132,930 (155)

On the sectional curvature of compact hypersurfaces [PDF]

open access: bronzeProceedings 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
openaire   +3 more sources

Group-Quotients with Positive Sectional Curvatures [PDF]

open access: bronzeProceedings 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
openaire   +3 more sources

Four-manifolds of pinched sectional curvature

open access: yesPacific 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
openaire   +3 more sources

On the scalar curvature and sectional curvatures of a Kaehler submanifold [PDF]

open access: yesProceedings 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.
Koichi Ogiue, Bang-yen Chen
openaire   +2 more sources

Sweeping out sectional curvature [PDF]

open access: yesGeometry & 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.
openaire   +7 more sources

Sectional curvature and Weitzenbock formulae

open access: yesIndiana 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.
openaire   +3 more sources

Strongly positive curvature [PDF]

open access: yes, 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

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