Geometric Mechanics on Warped Product Semi-Slant Submanifold of Generalized Complex Space Forms

In this study, we develop a general inequality for warped product semi-slant submanifolds of type M n = N T n 1 × f N ϑ n 2 in a nearly Kaehler manifold and generalized complex space forms using the Gauss equation instead of the Codazzi equation. There are several applications that can be developed from this. It is also described how to classify warped product semi-slant submanifolds that satisfy the equality cases of inequalities (determined using boundary conditions). Several results for connected, compact warped product semi-slant submanifolds of nearly Kaehler manifolds are obtained, and they are derived in the context of the Hamiltonian, Dirichlet energy function, gradient Ricci curvature, and nonzero eigenvalue of the Laplacian of the warping functions.

A β-tensor on Kaehler manifolds and its geometric characterizations

In this paper, we first introduce a new notion [Formula: see text]-tensor on Hermitian manifold and particularly, we present some geometric characterizations of such a tensor on the Kaehler manifold. Here, we investigate the Kaehler submersion whose total space is equipped with the [Formula: see text]-tensor and obtain some results. Also, we deal with a Kaehler submersion with totally geodesic fibers such that the total space admits [Formula: see text]-Ricci soliton and [Formula: see text]-tensor. Finally, we give necessary conditions for which any fiber and base manifold of Kaehler submersion is [Formula: see text]-Ricci soliton or [Formula: see text]-Kaehler-Einstein.

ANTI-INVARIANT RIEMANNIAN SUBMERSIONS FROM LOCALLY CONFORMAL KAEHLER MANIFOLDS

Recently, Sahin [10] studied the anti-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. In present work, these notions of anti-invariant and Lagrangian Riemannian submersions have been extended to locally conformal Kaehler manifolds. Certain decomposition results and the geometry of foliation have also been investigated.

B.-Y. Chen’s inequality for pointwise CR-slant warped products in cosymplectic manifolds

Recently, pointwise CR-slant warped products introduced by Chen and Uddin in [14] for Kaehler manifolds. In the context of almost contact metric manifolds, in this paper, we study these submanifolds in cosymplectic manifolds. We investigate the geometry of such warped product and prove establish a lower bound relation between the second fundamental form and warping function. The equality case is also investigated.