A characterization of homogeneous totally real minimal two-spheres in a complex hyperquadric

Abstract

In this paper, we give a characterization of homogeneous totally real minimal two-spheres in a complex hyperquadric [Formula: see text]. Let [Formula: see text] be a totally real minimal immersion from two-sphere in [Formula: see text], and [Formula: see text] (see Sec. 2) are globally defined invariants relative to the first and second fundamental forms. We prove that if its Gauss curvature [Formula: see text] and [Formula: see text] are constants, and [Formula: see text] vanishes identically, then [Formula: see text] is congruent to [Formula: see text] constructed by the Boruvka spheres with [Formula: see text].