Classification of semi-parallel hypersurfaces of the product of two spheres

Abstract

It is known that Mendonça and Tojeiro (2013) [19] have established a complete classification of parallel submanifolds in the product manifold Qk1n1×Qk2n2, where Qk1n1 (resp. Qk2n2) is an n1-dimensional (resp. n2-dimensional) real space form with constant curvature k1 (resp. k2). In this paper, motivated by this result with considering further generalization, we study those semi-parallel hypersurfaces in case Qk1n1=Sk1n1 and Qk2n2=Sk2n2 with k1,k2>0. As the main result, we classify semi-parallel hypersurfaces of Sk1n1×Sk2n2 for n1,n2≥2.