Warped Product Pointwise Semi-slant Submanifolds of Kaehler Manifolds

Abstract

It is known that there exist no warped product semi-slant submanifolds in Kaehler manifolds \cite{Sahin}. Recently, Chen and Garay studied pointwise-slant submanifolds of almost Hermitian manifolds in \cite{CG} and obtained many new results for such submanifolds. In this paper, we first introduce pointwise semi-slant submanifolds of Kaehler manifolds and then we show that there exists non-trivial warped product pointwise semi-slant submanifolds of Kaehler manifold by giving an example, contrary to the semi-slant case. We present a characterization theorem and establish an inequality for the squared norm of the second fundamental form in terms of the warping function for such warped product submanifolds in Kaehler manifolds. The equality case is also considered.

17 Pages, The final version will appear in Portugaliae Mathematica

Cited by in corpus (6)

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• Geometry of warped product and CR-warped product submanifolds in Kaehler manifolds: modified version
• Warped Product Pointwise Semi-slant Submanifolds of Almost Contact Manifolds
• Pointwise almost h-semi-slant submanifolds
• Geometry of pointwise semi-slant warped products in locally conformal Kaehler manifolds
• Geometry of $CRS$ bi-warped product submanifolds in Sasakian and cosymplectic manifolds