Warped Product Pointwise Semi-slant Submanifolds of Kaehler Manifolds

By Bayram Sahin. 2013

84 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f8b2ceed0982d6d3d479788b978da4f0b6717d15

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In Applied Mathematics

1. Siraj Uddin
2. Bang‐Yen Chen
3. Ion Mihai
4. Bayram Sahin
5. I. Hasegawa

In Geometry and Topology

1. Siraj Uddin
2. Bang‐Yen Chen
3. Ion Mihai
4. I. Hasegawa

Citations in the corpus

• Warped Product Pointwise Bi-slant Submanifolds of Kaehler Manifolds (2017, background): “Also, if θ1 = 0 and θ2 = θ, a slant function, then the submanifold M becomes pointwise semi-slant, which has been studied in [23].”