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Geometric inequalities for CR-warped product submanifolds of locally conformal almost cosymplectic manifolds

Ali Akram (Department of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia)
Othman Wan Ainun Mior (Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur, Malaysia)
Qasem Sayyadah A. (Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur, Malaysia)

In this paper, we establish some inequalities for the squared norm of the second fundamental form and the warping function of warped product submanifolds in locally conformal almost cosymplectic manifolds with pointwise φ-sectional curvature. The equality cases are also considered. Moreover, we prove a triviality result for CR-warped product submanifold by using the integration theory on a compact orientate manifold without boundary.

Keywords: Inequalities, compact CR-warped product submanifolds, locally confromal almost cosymplecric manifolds