Abstract
A submanifold M of an almost Hermitian manifold \((\widetilde{M},g,J)\) is called slant, if for each point \(p\in M\) and \(0\ne X\in T_p M\), the angle between JX and \(T_p M\) is constant (see Chen in Bull Aust Math Soc 41:135–147, 1990). Later, Carriazo (in: Proceedings of the ICRAMS 2000, Kharagpur, 2000) defined the notion of bi-slant immersions as an extension of slant immersions. In this paper, we study warped product bi-slant submanifolds in Kaehler manifolds and provide some examples of warped product bi-slant submanifolds in some complex Euclidean spaces. Our main theorem states that every warped product bi-slant submanifold in a Kaehler manifold is either a Riemannian product or a warped product hemi-slant submanifold.
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Acknowledgements
The authors thank the reviewers for their valuable suggestions to improve the presentation of this paper. The research was supported by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, under grant no. G-632-130-37. The authors, therefore, acknowledge with thanks DSR for technical and financial support.
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Uddin, S., Chen, BY. & Al-Solamy, F.R. Warped Product Bi-slant Immersions in Kaehler Manifolds. Mediterr. J. Math. 14, 95 (2017). https://doi.org/10.1007/s00009-017-0896-8
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DOI: https://doi.org/10.1007/s00009-017-0896-8
Keywords
- Warped product
- slant submanifolds
- bi-slant submanifolds
- warped product bi-slant submanifolds
- Kaehler manifolds