WARPED PRODUCT SEMI-INVARIANT SUBMANIFOLDS IN LOCALLY DECOMPOSABLE RIEMANNIAN MANIFOLDS

Abstract

Warped product semi-invariant submanifolds were defined and studied in locally Riemannian product manifolds in (K. Matsumoto, On submanifolds of locally product Riemannian manifolds, TRU Math. 18 (2), 145–157, 1982). In this paper, we go on to study warped product semi-invariant submanifolds in locally decomposable Riemannian manifolds. We prove several fundamental properties of warped product semi-invariant submanifolds, and establish a general inequality for a warped product semi-invariant submanifold in a locally decomposableRiemannian manifold. After that, we investigate warped product semiinvariant submanifolds in a locally decomposable Riemannian manifold which satisfy the equality case of the inequality and obtain some new results.