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Parallel submanifolds of complex space forms II

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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This is a continuation of Part I, which appeared in this journal.

In the previous paper I we have defined the following notions: orthogonal Jordan triple system (OJTS), orthogonal symmetric graded Lie algebra (OSGLA), orthogonal Jordan algebra (OJA), Hermitian symmetric graded Lie algebra (HSGLA). And we have shown that equivalent classes of OJTS naturally correspond to equivalent classes of OSGLA and through this correspondence we have naturally constructed HSGLA’s from the OJTS’s associated with OJA’s with unity.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 91 , September 1983 , pp. 119 - 149
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1983

References

[1] Berger, M., Espaces symétriques non compacts, Ann. Sci. École Norm. Sup. (3), 74 (1957), 85–177.CrossRefGoogle Scholar
[2] Cahen, M. and Parker, M., P seudo-riemannian symmetric spaces, Memo, of the Amer. Math. Soc, No. 229, 24 (1980).Google Scholar
[3] Ferus, D., Symmetric submanifolds of euclidean space, Math. Ann., 247 (1980), 81–93.Google Scholar
[4] Ferus, D.,Immersionen mit paralleler zweiter Fundamentalform : Beispiele und NichtBeispiele, Manuscripta Math., 12 (1974), 153–162.CrossRefGoogle Scholar
[5] Helgason, S., Differential geometry, Lie groups and Symmetric spaces, Academic Press, New York, 1978.Google Scholar
[6] Kobayashi, S. and Nagano, T., On filtered Lie algebras and geometric structures I, J. Math, and Mech., 13 (1964), 875–907.Google Scholar
[7] Kobayashi, S. and Nomizu, K., Foundations of Differential geometry I, II, Wiley (Interscience), 1963 and 1969.Google Scholar
[8] Naitoh, H., Totally real parallel submanifolds in Pn(c), Tokyo J. Math., 4, No. 2(1981), 279–306.Google Scholar
[9] Naitoh, H., Parallel submanifolds of complex space forms I, Nagoya Math. J., 90 (1983), 85–117.Google Scholar
[10] Naitoh, H. and Takeuchi, M., Totally real submanifolds and symmetric bounded domains, Osaka J. Math., 19 (1982), 717–731.Google Scholar
[11] Satake, I., Algebraic structures of symmetric domains, Iwanami Shoten, Publishers and Princeton Univ. Press, 1981.Google Scholar
[12] Takeuchi, M., Parallel submanifolds of space forms. In: Manifolds and Lie groups, in honor of Y. Matsushima, 429–447. Progress in Math., Vol. 14, Birkhäuser, 1981.Google Scholar