منابع مشابه
Wrapping spheres with flat paper
We study wrappings of smooth (convex) surfaces by a flat piece of paper or foil. Such wrappings differ from standard mathematical origami because they require infinitely many infinitesimally small folds (“crumpling”) in order to transform the flat sheet into a surface of nonzero curvature. Our goal is to find shapes that wrap a given surface, have small area and small perimeter (for efficient m...
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The condition for the vanishing of the Weyl tensor is integrated in the spherically symmetric case. Then, the resulting expression is used to find new, conformally flat, interior solutions to Einstein equations for locally anisotropic fluids. The slow evolution of these models is contrasted with the evolution of models with similar energy density or radial pressure distribution but non-vanishin...
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We define a large class of integrable nonlinear PDE’s, k-symmetric AKS systems, whose solutions evolve on finite dimensional subalgebras of loop algebras, and linearize on an associated algebraic curve. We prove that periodicity of the associated algebraic data implies a type of quasiperiodicity for the solution, and show that the problem of isometrically immersing n-dimensional Euclidean space...
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The structure theory ([3], [8]) for complete flat homogeneous pseudo-riemannian manifolds reduces the classification to the solution of some systems of quadratic equations. There is no general theory for that, but new solutions are found here by essentially the same construction as that used for isoclinic spheres in Grassmann manifolds [4]. It is interesting to speculate on a possible direct ge...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1969
ISSN: 0026-2285
DOI: 10.1307/mmj/1029000211