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Local rigidity theorems of 2-type hypersurfaces in a hypersphere
Published online by Cambridge University Press: 22 January 2016
Extract
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).
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1991
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