Results 281 to 290 of about 28,093 (313)

Sectional Curvatures and Characteristic Classes

The Annals of Mathematics, 1964
We are concerned here with the relationship between the curvature properties of a riemannian manifold X and the global topological and differential invariants of X. An interesting result in this direction is Chern's theorem [6] that if X is compact, orientable, and has constant riemannian sectional curvature, then all Pontrjagin classes of X (with real
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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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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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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 and tidal accelerations

Journal of Mathematical Physics, 1990
Sectional curvature is related to tidal accelerations for small objects of nonzero rest mass. Generically, the magnification of tidal accelerations due to high speed goes as the square of the magnification of energy. However, some space-times have directions with bounded increases in tidal accelerations for relativistic speeds.
Beem, John K., Parker, Phillip E.
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Sectional curvature in general relativity

General Relativity and Gravitation, 1987
This paper gives a detailed account of the sectional curvature function in general relativity from both the mathematical and the physical viewpoint. Some recent results are rederived by more systematic methods and some new results are obtained. Symmetries of the sectional curvature are also considered, as is the topological structure of the space of ...
Hall, G. S., Rendall, A. D.
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Sectional-curvature preserving skinning surfaces

Computer Aided Geometric Design, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kaklis, P. D., Ginnis, A. I.
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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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Sectional curvatures in nonlinear optimization

Journal of Global Optimization, 2007
Let \(M[h]=\{ x\in\mathbb R^n: h_j(x)=0\), \(j=1,\dots,n-k \}\), where \(k>0\), \(h_j \in C^2\) \((j=1, \dots,n-k)\). Suppose that the Jacobian matrix \(Jh(x)\) of \(h\) at \(x\) is of rank \(n-k\) for all \(x \in M[h]\). The author gives an explicit expression for the sectional curvature \(K_{M[h]}(x_0,w_1,w_2)\) of the manifold \(M[h]\) at a point ...
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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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