Results 201 to 207 of about 136,858 (207)
Some of the next articles are maybe not open access.
Sectional-curvature preserving skinning surfaces
Computer Aided Geometric Design, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kaklis, P. D., Ginnis, A. I.
openaire +1 more source
Sectional Curvature. Spaces of Constant Curvature. Weyl Hypothesis
1997As 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 ...
openaire +1 more source
Sectional curvatures in nonlinear optimization
Journal of Global Optimization, 2007Let \(M[h]=\{ x\in\mathbb R^n: h_j(x)=0\), \(j=1,\dots,n-k \}\), 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 ...
openaire +2 more sources
The geometry of sectional curvatures
General Relativity and Gravitation, 1976A 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 ...
openaire +1 more source