Slant Riemannian maps from almost Hermitian manifolds

As a generalization of holomorphic submersions, anti-invariant submersions and slant submersions, we introduce slant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds. We give examples, obtain the existence conditions of slant Riemannian maps and investigate harmonicity of such maps. We also obtain necessary and sufficient conditions for slant Riemannian maps to be totally geodesic and give a decomposition theorem for the total manifold.Comment: To appear in Quaestiones Mathematicae, 14 pages. arXiv admin note: text overlap with arXiv:1006.0081, arXiv:1206.339

Generic Riemannian maps

WOS: 000406745600041As a generalization of semi-invariant Riemannian maps from almost Hermitian mani-fols, we first introduce generic Riemannian maps from almost Hermitian manifolds to Riemannian manifolds, give examples, obtain decomposition theorems and investigate harmonicity and totally geodesicity of such maps. Then as a generalization of semi-invariant Riemannian maps to almost Hermitian manifolds, we introduce generic Riemannian maps from Riemannian manifolds to almost Hermitian manifolds, give examples and find necessary and sufficient conditions for such maps to be totally geodesic. The harmonicity of generic Riemannian maps to Kahler manifolds is also investigated

Skew CR-warped products of Kaehler manifolds

Warped product CR-submanifolds of Kaehler manifolds were introduced by Chen in [9]. In this paper, we introduce a warped product skew-CR-submanifold, which is a generalization of warped product CR-submanifolds. We give a characterization supported by an example and obtain an inequality in terms of the length of the second fundamental form of such submanifolds. The equality case is also investigated