Geometry of PR-warped products in para-Kaehler manifolds

Abstract

In this paper, we initiate the study of $\p R$-warped products in para-K\"ahler manifolds and prove some fundamental results on such submanifolds. In particular, we establish a general optimal inequality for $\p R$-warped products in para-K\"ahler manifolds involving only the warping function and the second fundamental form. Moreover, we completely classify $\p R$-warped products in the flat para-K\"ahler manifold with least codimension which satisfy the equality case of the inequality.