Proceedings of the American Mathematical Society

The indices, the nullities and the stability of totally geodesic submanifolds in the complex quadratic hypersurfaces: $Q_m=SO(m+2)/SO(m)\times SO(2)$

Author(s): Zhao Qiang
Journal: Proc. Amer. Math. Soc. 124 (1996), 2501-2512.
MSC (1991): Primary 53C35; Secondary 22E70
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Abstract: In the paper, the stability of totally geodesic submanfolds in the complex quadratic hypersurfaces: $Q_m=SO(m+2)/SO(m)\times SO(2) (m>1)$ is discussed, and the indices, the nullities and the Killing nullities of totally geodesic submanifolds in $Q_m$

are calculated.

1.: Y.Ohnita, On stability of minimal submanifolds in compact symmetric spaces, Compsitio Math., 64(1987), 157-189. MR 88k:53082
2.: B.Y.Chen, Geometry of slant submanifolds, Katholieke Universiteit Leuven, 1990. MR 92d:53047
3.: B.Y.Chen and T.Nagano, Totally geodesic submanifolds of symmetric spaces I, Duke Math. J., 44(1977), 745-755. MR 56:16543
4.: E.B.Dynkin, Semisimple subalgebras of semisimple Lie algebras, Amer. Math. Soc. Transl. Ser. 2, vol. 6, Amer. Math. Soc., Providence, RI, 1957, pp. 111-244. (Russian original) MR 13:904c
5.: W.G.Mckay and J.Patera, Tables of dimensions, indices, and branching rules for representations of simple Lie algebras, Lecture Notes in Pure and Applied Mathematics, vol. 69, Marcel Dekker, New York and Basel, 1981. MR 82i:17008

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 53C35, 22E70

Zhao Qiang
Affiliation: Department of Mathematics, Beijing University, Beijing, 100871, People's Republic of China - Department of Mathematics, Northwest Normal University, Lanzhou, 730070, People's Republic of China

DOI: 10.1090/S0002-9939-96-03313-8
PII: S 0002-9939(96)03313-8
Keywords: Indices, nullities, stability
Received by editor(s): August 5, 1994
Received by editor(s) in revised form: January 18, 1995
Communicated by: Roe W. Goodman
Copyright of article: Copyright 1996, American Mathematical Society

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