Results 231 to 240 of about 28,343 (263)

Cross-sectional design with curvature constraints

Computer-Aided Design, 2005
A practical example of B-spline curve control points manipulation for the geometric construction of a free form shape is presented. Elements of a cross-sectional design methodology are used in conjunction with a skinning type operator for the definition of a B-spline surface.
Anas Bentamy, François Guibault, Jean Yves Trépanier   +2 more
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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 curvature and the energy–momentum tensor

Classical and Quantum Gravity, 2005
\textit{J.~Ehlers and W.~Kundt} [Gravitation: An Introduction to Current Research, ed. L.~Witten, New York: Wiley, 1962, p. 49] showed that if \(M\) is a spacetime and \(p\in M\), the statement that the Einstein space condition holds at \(p\) is equivalent to the statement that the sectional curvatures of each of any orthogonal pair of non-null 2 ...
Hall, G. S., MacNay, Lucy
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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 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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