From symmetric to transsymmetric spaces
نویسندگان
چکیده
منابع مشابه
From Groups to Symmetric Spaces
This paper is based on a talk given at the conference ”Representation theory of real reductive groups”, Salt Lake City, July 2009. We fix an algebraically closed field k of characteristic exponent p. (We assume, except in §18, that either p = 1 or p ≫ 0.) We also fix a symmetric space that is a triple (G, θ,K) where G is a connected reductive algebraic group over k, θ : G −→ G is an involution ...
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In this paper we study generalized symmetric Berwald spaces. We show that if a Berwald space $(M,F)$ admits a parallel $s-$structure then it is locally symmetric. For a complete Berwald space which admits a parallel s-structure we show that if the flag curvature of $(M,F)$ is everywhere nonzero, then $F$ is Riemannian.
متن کاملGroups to Symmetric Spaces
This paper is based on a talk given at the conference ”Representation theory of real reductive groups”, Salt Lake City, July 2009. We fix an algebraically closed field k of characteristic exponent p. (We assume, except in §17, that either p = 1 or p ≫ 0.) We also fix a symmetric space that is a triple (G, θ,K) where G is a connected reductive algebraic group over k, θ : G −→ G is an involution ...
متن کاملSymmetric Spaces
Notations M Riemannian manifold. N 0 normal neighborhood of the origin in T p M. N p normal neighbourhood of p, N p = exp N 0. s p geodesic symmetry with respect to p. f Φ d Φ f = f • Φ. X Φ d Φ X. K(S) sectional curvature of M at p along the section S. D r s set of tensor fields of type (r, s). I(M) the set of all isometries on M Definition 1 (normal neighborhood) A neighborhood N p of p in M ...
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Let θ : g → g be an involution of a complex semisimple Lie algebra, k ⊂ g the fixed points of θ, and V = g/k the corresponding symmetric space. The adjoint form K of k naturally acts on V . The orbits and invariants of this representation were studied by Kostant and Rallis in [KR]. Let X = K\\V be the invariant theory quotient, and f : V → X be the quotient map. The space X is isomorphic to C. ...
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ژورنال
عنوان ژورنال: Differential Geometry and its Applications
سال: 2002
ISSN: 0926-2245
DOI: 10.1016/s0926-2245(02)00107-9