Results 201 to 210 of about 138,464 (231)

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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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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GENERAL RELATIVITY AND SECTIONAL CURVATURE

International Journal of Geometric Methods in Modern Physics, 2006
A discussion is given of the sectional curvature function on a four-dimensional Lorentz manifold and, in particular, on the space–time of Einstein's general relativity theory. Its tight relationship to the metric tensor is demonstrated and some of its geometrical and algebraic properties evaluated.
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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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Sectional-curvature preserving skinning surfaces

Computer Aided Geometric Design, 1996
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Panagiotis D. Kaklis, Alexandros I. Ginnis   +1 more
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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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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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Pinching the Sectional Curvature on Open Manifolds

The Journal of Geometric Analysis, 2017
In this paper, the author proves the following theorem: Theorem. Let \(M\) be an open manifold. Given \(\delta >0\) and \(a\in R\), there exists a Riemannian metric on \(M\) such that all sectional curvatures are in \((a-\delta, a+\delta)\).
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Norden Golden Manifolds with Constant Sectional Curvature and Their Submanifolds

Mathematics, 2023
Fulya Sahin, Bayram Sahin, Feyza Esra Erdogan   +2 more
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