Isometric immersions of higher codimension into the product S k × H n+p−k

In this paper, we obtain a sufficient and necessary condition for a simply connected Riemannian manifold (Mn, g) to be isometrically immersed, as a submanifold with codimension p ≥ 1, into the product Sk × Hn+p−k of sphere and hyperboloid.