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Symmetric space - Wikipedia

http://www.cms.zju.edu.cn/UploadFiles/AttachFiles/200471118586485.pdf WebThis unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincaré upper half plane. This book is intended for beginning graduate students in … jedrick wills alabama photo

On compact minimal hypersurfaces in a sphere with constant …

Symmetric and locally symmetric spaces in general can be regarded as affine symmetric spaces. If M = G / H is a symmetric space, then Nomizu showed that there is a G -invariant torsion-free affine connection (i.e. an affine connection whose torsion tensor vanishes) on M whose curvature is parallel . Zobraziť viac In mathematics, a symmetric space is a Riemannian manifold (or more generally, a pseudo-Riemannian manifold) whose group of symmetries contains an inversion symmetry about every point. This can be studied with the … Zobraziť viac Let M be a connected Riemannian manifold and p a point of M. A diffeomorphism f of a neighborhood of p is said to be a geodesic symmetry if it fixes the point p and reverses geodesics through that point, i.e. if γ is a geodesic with Zobraziť viac The algebraic description of Riemannian symmetric spaces enabled Élie Cartan to obtain a complete classification of them in 1926. Zobraziť viac An important class of symmetric spaces generalizing the Riemannian symmetric spaces are pseudo-Riemannian symmetric spaces, in which the Riemannian metric is replaced by a pseudo-Riemannian metric (nondegenerate instead of positive definite on each … Zobraziť viac Let G be a connected Lie group. Then a symmetric space for G is a homogeneous space G/H where the stabilizer H of a typical point is an open subgroup of the fixed point set of … Zobraziť viac If M is a Riemannian symmetric space, the identity component G of the isometry group of M is a Lie group acting transitively on M (that is, M is Riemannian homogeneous). … Zobraziť viac In the 1950s Atle Selberg extended Cartan's definition of symmetric space to that of weakly symmetric Riemannian space, or in current … Zobraziť viac WebA spherically symmetric spacetime is a spacetime whose isometry group contains a subgroup which is isomorphic to the rotation group SO(3) and the orbits of this group are … Web2, the standard metric on the 2–sphere, is an abbreviation for d 2 + sin2 d˚2 (or more symmetrically for P 3 j=1 dz 2 j restricted to P 3 j=1 z 2 j = 1). These metrics are all spherically-symmetric and represent locally the general spherically-symmetric space-time. A significant subclass is when P and Q are functions of t alone. In this ... jedrick wills twitter