Complex-symmetric spaces
نویسندگان
چکیده
منابع مشابه
Complex Forms of Quaternionic Symmetric Spaces
Some years ago, H. A. Jaffee found the real forms of Hermitian symmetric spaces ([J1], [J2]; or see [HÓ]). That classification turns out to be related to the classification of causal symmetric spaces. This was first observed by I. Satake ([S, Remark 2 on page 30] and [S, Remark on page 87]). Somewhat later, it was independently observed by J. Hilgert, G. Ólafsson and B. Ørsted; see [HÓ], especi...
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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.
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Roger W. Richardson proved that any parabolic subgroup of a complex semisimple Lie group admits an open dense orbit in the nilradical of its corresponding parabolic subalgebra. In the case of complex symmetric spaces we show that there exist some large classes of parabolic subgroups for which the analogous statement which fails in general, is true. Our main contribution is the extension of a th...
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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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This paper contains a thorough study of the trigonometry of the homogeneous symmetric spaces in the Cayley-Klein-Dickson family of spaces of 'complex Hermitian' type and rank-one. The complex Hermitian elliptic CP are the generic members in this family; the remaining spaces are some contractions of the former. The method encapsulates trigonometry for this whole family of spaces into a single ba...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 1989
ISSN: 0373-0956
DOI: 10.5802/aif.1171