Rigidity of minimal hypersurfaces of spheres with
two principal curvatures |
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Authors: | Email author" target="_blank">O?PerdomoEmail author |
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Institution: | (1) Departamento de Matematicas, Universidad del Valle, Cali, Colombia |
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Abstract: | Let M be a compact oriented minimal
hypersurface of the unit n-dimensional sphere
Sn.
It is known that if the norm squared of the second fundamental form,
, satisfies that
for all
, then M is isometric to a Clifford
minimal hypersurface (2], 5]). In this paper we will generalize this result
for minimal hypersurfaces with two principal curvatures and dimension greater
than 2. For these hypersurfaces we will show that if the average of the function
is n - 1, then M
must be a Clifford hypersurface.
Received: 24 December 2002 |
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Keywords: | 53C42 53A10 |
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