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Local rigidity theorems of 2-type hypersurfaces in a hypersphere

Published online by Cambridge University Press:  22 January 2016

Bang-Yen Chen
Bang-Yen Chen*
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027, U.S.A.
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A submanifold M (connected but not necessary compact) of a Euclidean m-space Em is said to be of finite type if each component of its position vector X can be written as a finite sum of eigenfunctions of the Laplacian Δ of M, that is,

where X0 is a constant vector and ΔXt = λtXt, t = 1, 2, · · ·, k. If in particular all eigenvalues {λ1, λ2, · · ·, λk are mutually different, then M is said to be of k-type (cf. [3] for details).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 122 , June 1991 , pp. 139 - 148
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1991

References

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