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On compact minimal hypersurfaces in a sphere with constant scalar curvature

Published online by Cambridge University Press:  22 January 2016

Naoya Doi
Naoya Doi*
Affiliation:
Department of Mathematics, Nagoya University
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Let M be an n-dimensional hypersurface immersed in the (n + 1)-dimensional unit sphere Sn+1 with the standard metric by an immersion f. We denote by A the second fundamental form of the immersion / which is considered as a symmetric linear transformation of each tangent space TXM, i.e. for an arbitrary point x of M and the unit normal vector field ξ defined in a neighborhood of x, A is given by where is the covariant differentiation in Sn+i and Thus, A depends on the orientation of the unit normal vector field ξ and, in general, it is locally defined on M.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 78 , May 1980 , pp. 177 - 188
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1980

References

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