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Mathematica Slovaca

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Volume 61, Issue 1


A note on warped product submanifolds of Kenmotsu manifolds

Viqar Khan / Khalid Khan / Siraj-Uddin
Published Online: 2011-01-26 | DOI: https://doi.org/10.2478/s12175-010-0061-3


Warped product manifolds are known to have applications in Physics. For instance, they provide an excellent setting to model space-time near a black hole or a massive star (cf. [HONG, S. T.: Warped products and black holes, Nuovo Cimento Soc. Ital. Fis. B 120 (2005), 1227–1234]). The studies on warped product manifolds with extrinsic geometric point of view are intensified after B. Y. Chen’s work on CR-warped product submanifolds of Kaehler manifolds. Later on, similar studies are carried out in the setting of Sasakian manifolds by Hasegawa and Mihai. As Kenmotsu manifolds are themselves warped product spaces, it is interesting to investigate warped product submanifolds of Kenmotsu manifolds. In the present note a larger class of warped product submanifolds than the class of contact CR-warped product submanifolds is considered. More precisely the existence of warped product submanifolds of a Kenmotsu manifold with one of the factors an invariant submanifold is ensured, an example of such submanifolds is provided and a characterization for a contact CR-submanifold to be a contact CR-warped product submanifold is established.

MSC: Primary 53C40, 53C42; Secondary 53B25

Keywords: warped product; generic warped product; semi-slant submanifold; Kenmotsu manifold

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About the article

Published Online: 2011-01-26

Published in Print: 2011-02-01

Citation Information: Mathematica Slovaca, Volume 61, Issue 1, Pages 79–92, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.2478/s12175-010-0061-3.

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© 2011 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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