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A decomposition theorem of 2-type immersions

Published online by Cambridge University Press:  22 January 2016

Motoko Kotani
Motoko Kotani*
Affiliation:
Department of Mathematics, Tokyo Metropolitan University, Fukasawa, Setagaya, Tokyo 158, Japan
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One branch of the research of submanifolds was introduced by Chen in terms of type in [2]. Type of a submanifold makes clear how the eigenspace decomposition of the Laplacian (of the ambient space) preserve after restricted to the submanifold.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 118 , June 1990 , pp. 55 - 64
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1990

References

[1] Barros, M. and Chen, B. Y., Spherical submanifolds which are of 2-type via the second standard immersion of the sphere, Nagoya Math. J., 108 (1987), 77–91.Google Scholar
[2] Chen, B. Y., Total mean curvature and submanifolds of finite type, World Scientific, 1984.Google Scholar
[3] Chern, S. S., On the minimal immersions of the two-sphere in a space of constant curvature, Problems in analysis, A symposium in hornor of Salomon Bochner, Princeton University Press (1970).Google Scholar
[4] Takahashi, T., Minimal immersions of riemannian manifolds, J. Math. Soc. Japan, 18 (1966), 380–385.Google Scholar
[5] Ros, A., On spectral geometry of Kaehler submanifolds, J. Math. Soc. Japan, 36 (1984), 433–447.Google Scholar