Lagrangian Submanifolds with Constant Angle functions of the Nearly Kähler S3 × S3

Abstract

We study Lagrangian submanifolds of the nearly Kähler S3 × S3 with respect to their so called angle functions. We show that if all angle functions are constant, then the submanifold is either totally geodesic or has constant sectional curvature and there is a classification theorem that follows from Dioos et al. (2018). Moreover, we show that if precisely one angle function is constant, then it must be equal to 0, π 3 or 2π 3 . Using then two remarkable constructions together with the classification of Lagrangian submanifolds of which the first component has nowhere maximal rank from, Bektaş et al. (2018), we obtain a classification of such Lagrangian submanifolds.