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On some submanifolds of Kenmotsu manifolds

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  • Sular, Si˙bel
  • Özgür, Ci˙han

Abstract

In this paper, we study submanifolds of Kenmotsu manifolds. We prove that if the second fundamental form of a submanifold of a Kenmotsu manifold is recurrent, 2-recurrent or generalized 2-recurrent then the submanifold is totally geodesic. Furthermore, we show that a submanifold of a Kenmotsu manifold with parallel third fundamental form is again totally geodesic. We also consider quasi-umbilical hypersurfaces of Kenmotsu space forms. We show that these type hypersurfaces are generalized quasi-Einstein.

Suggested Citation

  • Sular, Si˙bel & Özgür, Ci˙han, 2009. "On some submanifolds of Kenmotsu manifolds," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 1990-1995.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:4:p:1990-1995
    DOI: 10.1016/j.chaos.2009.03.185
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    References listed on IDEAS

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    1. El Naschie, M.S., 2006. "Is Einstein’s general field equation more fundamental than quantum field theory and particle physics?," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 525-531.
    2. El Naschie, M.S., 2005. "Gödel universe, dualities and high energy particles in E-infinity," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 759-764.
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