منابع مشابه
Symmetric Submanifolds of Riemannian Symmetric Spaces
A symmetric space is a Riemannian manifold that is “symmetric” about each of its points: for each p ∈M there is an isometry σp of M such that (σp)∗ = −I on TpM . Symmetric spaces and their local versions were studied and classified by E.Cartan in the 1920’s. In 1980 D.Ferus [F2] introduced the concept of symmetric submanifolds of Euclidean space: A submanifold M of R is a symmetric submanifold ...
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In the first part of this expository article, the most important constructions and classification results concerning totally geodesic submanifolds in Riemannian symmetric spaces are summarized. In the second part, I describe the results of my classification of the totally geodesic submanifolds in the Riemannian symmetric spaces of rank 2. To appear in the Proceedings volume for the conference V...
متن کاملGeneralized Symmetric Berwald Spaces
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 کاملOn submanifolds in locally symmetric spaces of noncompact type
Given a connected, compact, totally geodesic submanifold Ym of noncompact type inside a compact locally symmetric space of noncompact type Xn , we provide a sufficient condition that ensures that [Ym] 6= 0 ∈ Hm(X; R); in low dimensions, our condition is also necessary. We provide conditions under which there exist a tangential map of pairs from a finite cover (X̄, Ȳ) to the nonnegatively curved ...
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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ژورنال
عنوان ژورنال: Differential Geometry and its Applications
سال: 2002
ISSN: 0926-2245
DOI: 10.1016/s0926-2245(01)00069-9