Hypersurfaces of the sphere S6(1) with four-dimensional nullity distribution

Abstract

The sphere S⁶(1) is one of the four homogeneous, six-dimensional nearly Kähler manifolds, and the only one where the nearly Kähler structure is given with the standard metric. A nullity distribution of a submanifold consists of the vector fields $X$ such that the second fundamental form $h$ satisfies $h(X, .)=0$. The totally geodesic sphere S⁶ trivially admits a five-dimensional nullity distribution. In this paper, we investigate non totally geodesic hypersurfaces of the nearly Kähler sphere S⁶(1), that admit nullity distribution of the maximal possible dimension, i.e. with nullity distribution of the dimension four and classify them.