Results 271 to 280 of about 1,470,963 (294)

Sectional Curvature Comparison II

1998
In the previous chapter we classified complete spaces with constant curvature. The goal of this chapter is to compare manifolds with variable curvature to spaces with constant curvature. Our first global result is the Hadamard-Cartan theorem, which says that a simply connected complete manifold with \(\sec \leq 0\) is diffeomorphic to \(\mathbb{R}^{n}\)
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The geometry of sectional curvatures

General Relativity and Gravitation, 1976
A large class of questions in differential geometry involves the relationship between the geometry and the topology of a Riemannian (= positive-definite) manifold. We briefly review the status of the following question from this class: given that a compact, even-dimensional manifold admits a Riemannian metric of positive sectional curvatures, what can ...
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Negative ξ-sectional Curvature

2002
The purpose of this chapter is to introduce some special directions that belong to the contact subbundle of a contact metric manifold with negative sectional curvature for plane sections containing the characteristic vector field ξ or more generally when the operator h admits an eigenvalue greater than 1; these directions were introduced by the author ...
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Vertical sectional curvature and K-contactness

Journal of Geometry, 1995
Let \((M, \alpha)\) be a contact manifold. The contact form \(\alpha\) is said to be \(K\)-contact if there exists a contact metric \(g\) which is invariant under the characteristic vector field \(v\) of \(\alpha\), i.e. \({\mathcal L}_v g= 0\). The author writes that there seems to be a confusion in the literature whether or not the requirement on \(g\
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Sectional Curvature. Spaces of Constant Curvature. Weyl Hypothesis

1997
As we have seen, by introducing the notion of curvature tensor K ∇, with any pair of tangent vectors Y, Z ∈ T x M we associated a linear transformation K x (Y, Z) of the tangent space T x M. Let F x be an oriented plane spanned by Y, Z (that is, Y, Z are basis vectors in F x .) Let S F be a surface (in M) generated by geodesics tangent to F, more ...
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Damage detection of tunnel based on the high-density cross-sectional curvature obtained using strain data from BOTDA sensors

Mechanical Systems and Signal Processing, 2021

exaly  

On Hypersurfaces with no Negative Sectional Curvatures

American Journal of Mathematics, 1960
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Manifolds with positive sectional curvature almost everywhere

Inventiones Mathematicae, 2002
Burkhard Wilking
exaly  

Affine spheres with constant affine sectional curvature

Mathematische Zeitschrift, 1991
Luc Vrancken, Udo Simon, Vrancken Luc
exaly  

Kähler parabolicity and the Euler number of compact manifolds of non-positive sectional curvature

Mathematische Annalen, 2001
Frederico Xavier, Cao Jianguo, Xavier Frederico   +2 more
exaly