GEOMETRY OF PR-WARPED PRODUCTS IN PARA-KÄHLER MANIFOLDS

In this paper, we initiate the study of PR-warped products in para-Kähler manifolds and prove some fundamental results on such submanifolds. In particular, we establish a general optimal inequality for PR-warped products in para-Kähler manifolds involving only the warping function and the second fundamental form. Moreover, we completely classify PR-warped products in the flat para-Kähler manifold with least codimension which satisfy the equality case of the inequality. Our results provide an answer to the Open Problem (3) proposed in [19, Section 5]. 2010Mathematics Subject Classification: 53B25, 53B30, 53C15, 53C20. Key words and phrases: Para-Kähler manifold, PR-Submanifold, Warped product.