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Parallel submanifolds of complex space forms I

Published online by Cambridge University Press:  22 January 2016

Hiroo Naitoh
Hiroo Naitoh*
Affiliation:
Department of Mathematics, Yamaguchi University, Yamaguchi, 753, Japan
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Complete parallel submanifolds of a real space form of constant sectional curvature k have been completely classified by Ferus [3] when k ≧ 0, and by Takeuchi [19] when k < 0. A complex space form is by definition a 2n-dimensional simply connected Hermitian symmetric space of constant holomorphic sectional curvature c and will be denoted by (c).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 90 , June 1983 , pp. 85 - 117
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1983

References

[ 1 ] Chen, B. Y.-Ogiue, K., On totally real submanifolds, Trans. Amer. Math. Soc, 193 (1974), 257–266.Google Scholar
[ 2 ] Dombrowski, P., Differentiable maps into riemannian manifolds of constant stable osculating rank I, J. Reine Angew. Math., 274/275 (1975), 310–341.Google Scholar
[ 3 ] Ferus, D., Symmetric submanifolds of euclidean space, Math. Ann., 247 (1980), 81–93.Google Scholar
[ 4 ] Ferus, D., Immersions with parallel second fundamental form, Math. Z., 140 (1974), 87–93.Google Scholar
[ 5 ] Ferus, D., Immersionen mit paralleler zweiter Fundamentalform : Beispiele und Nicht-Beispiele, Manuscripta Math., 12 (1974), 153–162.Google Scholar
[ 6 ] Helgason, S., Differential Geometry, Lie groups and Symmetric spaces, Academic Press, New York, 1978.Google Scholar
[ 7 ] Kobayashi, S. and Nomizu, K., Foundations of Differential geometry I, II, Wiley (Interscience), 1963 and 1969.Google Scholar
[ 8 ] Koecher, M., “An elementary approach to bounded symmetric domains”, Lect. Notes, Rice Univ., Houston, 1969.Google Scholar
[ 9 ] Kon, M., On some complex submanifolds in Kaehler manifolds, Canad. J. Math., 26 (1974), 1442–1449.Google Scholar
[10] Naitoh, H., Isotropic submanifolds with parallel second fundamental form in Pm(c), Osaka J. Math., 18 (1981), 427–464.Google Scholar
[11] Naitoh, H., Totally real parallel submanifolds in Pn(c), Tokyo J. Math., 4 (1981), 279–306.Google Scholar
[12] Naitoh, H. and Takeuchi, M., Totally real submanifolds and symmetric bounded domains, Osaka J. Math., 19 (1982), 717–731.Google Scholar
[13] Nakagawa, H. and Takagi, , On locally symmetric Kaehler submanifolds in a complex projective space, J. Math. Soc. Japan, 28 (1976), 638–667.Google Scholar
[14] O’Neill, B., The fundamental equations of a submersion, Michigan Math. J., 131 (1966), 459–469.Google Scholar
[15] Pak, J. S., Planar geodesic submanifolds in complex space forms, Kodai Math. J., 1 (1978),187–196.Google Scholar
[16] Satake, I., Algebraic structures of symmetric domains, Iwanami Shoten, Publishers and Princeton Univ. Press, 1981.Google Scholar
[17] Strübing, W., Symmetric Submanifolds of Riemannian Manifolds, Math. Ann., 245 (1979), 37–44.Google Scholar
[18] Takeuchi, M., Polynomial representations associated with symmetric bounded domains, Osaka J. Math., 10 (1973), 441–475.Google Scholar
[19] Takeuchi, M., Parallel submanifolds of space forms, In: Manifolds and Lie groups (Papers in honor of Matsushima, Y.), Birkhäuser, 1981.CrossRefGoogle Scholar