On compact minimal hypersurfaces in a sphere with constant scalar curvature
1980 ◽
Vol 78
◽
pp. 177-188
◽
Keyword(s):
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.
2017 ◽
Vol 35
(3)
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pp. 79-93
Keyword(s):
1992 ◽
Vol 34
(3)
◽
pp. 309-311
◽
2018 ◽
Vol 149
(2)
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pp. 279-296
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2021 ◽