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arXiv · 1708.05881

Virtual immersions and minimal hypersurfaces in compact symmetric spaces

Ricardo A. E. Mendes·Marco Radeschi
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Abstract

We show that closed, immersed, minimal hypersurfaces in a compact symmetric space satisfy a lower bound on the index plus nullity, which depends linearly on their first Betti number. Moreover, if either the minimal hypersurface satisfies a certain genericity condition, or if the ambient space is a product of two CROSSes, we improve this to a lower bound on the index alone, which is affine in the first Betti number. To prove these, we introduce a generalization of isometric immersions in Euclidean space. Compact symmetric spaces admit (and in fact are characterized by) such a structure with skew-symmetric second fundamental form.

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Ricardo A. E. Mendes, Marco Radeschi. 2017-08-19. Virtual immersions and minimal hypersurfaces in compact symmetric spaces. https://arxiv.org/abs/1708.05881

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