Minimal hypersurfaces in a nearly Kaehler 6-sphere

Abstract

In this paper we show that for a compact minimal hypersurface M of constant scalar curvature in the unit sphere S 6 with the shape operator A satisfying ‖ A ‖ 2 > 5 , there exists an eigenvalue λ > 10 of the Laplace operator of the hypersurface M such that ‖ A ‖ 2 = λ − 5 . This gives the next discrete value of ‖ A ‖ 2 greater than 0 and 5.