The Morse index of quartic minimal hypersurfaces

Author:

Gavin Ball, Jesse Madnick, Uwe Semmelmann

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG)

journal:

date:

2023-10-29 16:00:00

Abstract

The homogeneous minimal hypersurfaces in $S^n$ have $g = 1,2,3,4$, or $6$ distinct (constant) principal curvatures. While the Morse index and nullity have been calculated for all such hypersurfaces having $g = 1,2,3$, it has remained an open problem to compute these quantities for any of those with $g = 4$ or $6$. In this paper, we calculate the Morse index and nullity of two homogeneous minimal hypersurfaces in $S^n$ with $g = 4$. Moreover, we observe that their Laplace spectra contain irrational eigenvalues that are not expressible in radicals.

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