A note on warped product submanifolds of Kenmotsu manifolds

V A Khan, Khalid Khan, Siraj Uddin

    Research output: Contribution to journalArticleResearchpeer-review

    Abstract

    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.
    Original languageEnglish
    Pages (from-to)79-92
    Number of pages14
    JournalMathematica Slovaca
    Volume61
    Issue number1
    DOIs
    Publication statusPublished - 2011

    Fingerprint

    Warped Product
    Submanifolds
    Contact
    Black Holes
    Kaehler Manifold
    CR-submanifold
    Invariant Submanifold
    Sasakian Manifold
    Product Space
    Star
    Space-time
    Physics

    Cite this

    Khan, V A ; Khan, Khalid ; Uddin, Siraj. / A note on warped product submanifolds of Kenmotsu manifolds. In: Mathematica Slovaca. 2011 ; Vol. 61, No. 1. pp. 79-92.
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    A note on warped product submanifolds of Kenmotsu manifolds. / Khan, V A; Khan, Khalid; Uddin, Siraj.

    In: Mathematica Slovaca, Vol. 61, No. 1, 2011, p. 79-92.

    Research output: Contribution to journalArticleResearchpeer-review

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    AB - 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.

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