2023/10/30 by Ball, Gavin, Madnick, Jesse, Semmelmann, Uwe
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2310.19404
The homogeneous minimal hypersurfaces in Sn 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 Sn with g = 4. Moreover, we observe that their Laplace spectra contain irrational eigenvalues that are not expressible in radicals.