Kodai Mathematical Journal

Estimate for index of closed minimal hypersurfaces in spheres

Abdênago Alves de Barros and Paulo Alexandre Araújo Sousa

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Abstract

The aim of this work is to deal with index of closed orientable non-totally geodesic minimal hypersurface Σn of the Euclidean unit sphere Sn+1 whose second fundamental form has squared norm bounded from below by n. In this case we shall show that the index of stability, denoted by IndΣ, is greater than or equal to n + 3, with equality occurring at only Clifford tori $\mathbf{S}^k(\frac{k}{n})\times\mathbf{S}^{n-k}(\sqrt{\frac{(n-k)}{n}})$. Moreover, we shall prove also that, besides Clifford tori, we have the following gap: IndΣ ≥ 2n + 5.

Article information

Source
Kodai Math. J., Volume 32, Number 3 (2009), 442-449.

Dates
First available in Project Euclid: 11 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1257948889

Digital Object Identifier
doi:10.2996/kmj/1257948889

Mathematical Reviews number (MathSciNet)
MR2582011

Zentralblatt MATH identifier
1180.53064

Citation

de Barros, Abdênago Alves; Sousa, Paulo Alexandre Araújo. Estimate for index of closed minimal hypersurfaces in spheres. Kodai Math. J. 32 (2009), no. 3, 442--449. doi:10.2996/kmj/1257948889. https://projecteuclid.org/euclid.kmj/1257948889


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