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On Semi-Invariant Submanifolds of a Generalized Kenmotsu Manifold Admitting a Semi-Symmetric Non-Metric Connection

Received: 14 November 2014    Accepted: 20 November 2014    Published: 12 January 2015
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Abstract

In this paper, semi-invariant submanifolds of a generalized Kenmotsu manifold endowed with a semi-symmetric non-metric connection are studied. Necessary and sufficient conditions are given on a submanifold of a generalized Kenmotsu manifold to be semi-invarinat submanifold with semi-symmetric non-metric connection. Morever, we studied the integrability condition of the distribution on semi-invariant submanifolds of generalized Kenmotsu manifold with semi-symmetric non-metric connection.

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 1-2)

This article belongs to the Special Issue Applications of Geometry

DOI 10.11648/j.pamj.s.2015040102.14
Page(s) 14-18
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Generalized Kenmotsu Manifolds, Semi-Invariant Submanifolds, Semi-Symmetric Non-Metric Connection

References
[1] D.E. Blair , Geometry of manifolds with structural group U(n) x O(s), J. Differ. Geom. 4, 155-167 (1970).
[2] K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J. 24 (1972) 93-103.
[3] M. Kobayashi, Semi-invariant submanifolds of a certain class of almost contact manifolds, Tensor N. S. 43 (1986) 28-36.
[4] S. Goldberg and K. Yano, Globally framed f-Manifolds, Illinois J. Math.15, 456-474 (1971).
[5] S. A. Nirmala and R.C. Mangala, a semi-symmetric non-metric connection on Riemannian manifold, Indiana J. Pure Appl. Math. 23 399-409 (1992).
[6] B. Prasad, Semi-invariant submanifolds of a Lorentzian para-Sasakian manifold, Bull. Malaysian Math. Soc. 21 (1998) 21-26.
[7] B. B. Sinha and A. K. Srivastava, Semi-invariant submanifolds of a Kenmotsu manifold with constant φ-holomorphic sectional curvature, Indian J. pure appl. Math. 23(11):783-789 (1992).
[8] M. M. Tripathi, A new connection in a Riemannian manifold, Int. Ele.Journal of Geometry Vol.1 No.1 15-24 (2008).
[9] A Turgut Vanli and R. Sari , Generalized Kenmotsu manifolds, Arxiv 1406.1032v1.
[10] J. Vanzura, Almost r-contact structures, Ann. Scuola Norm. Sup. Pisa Sci. Fis. Mat. 26 (1972), 97–115.
[11] K. Yano, On a structure defined by a tensor field f of type (1, 1) satisfying f 3+f=0, Tensor NS., 14, 99-109 (1963) .
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  • APA Style

    Aysel Turgut Vanli, Ramazan Sari. (2015). On Semi-Invariant Submanifolds of a Generalized Kenmotsu Manifold Admitting a Semi-Symmetric Non-Metric Connection. Pure and Applied Mathematics Journal, 4(1-2), 14-18. https://doi.org/10.11648/j.pamj.s.2015040102.14

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    ACS Style

    Aysel Turgut Vanli; Ramazan Sari. On Semi-Invariant Submanifolds of a Generalized Kenmotsu Manifold Admitting a Semi-Symmetric Non-Metric Connection. Pure Appl. Math. J. 2015, 4(1-2), 14-18. doi: 10.11648/j.pamj.s.2015040102.14

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    AMA Style

    Aysel Turgut Vanli, Ramazan Sari. On Semi-Invariant Submanifolds of a Generalized Kenmotsu Manifold Admitting a Semi-Symmetric Non-Metric Connection. Pure Appl Math J. 2015;4(1-2):14-18. doi: 10.11648/j.pamj.s.2015040102.14

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  • @article{10.11648/j.pamj.s.2015040102.14,
      author = {Aysel Turgut Vanli and Ramazan Sari},
      title = {On Semi-Invariant Submanifolds of a Generalized Kenmotsu Manifold Admitting a Semi-Symmetric Non-Metric Connection},
      journal = {Pure and Applied Mathematics Journal},
      volume = {4},
      number = {1-2},
      pages = {14-18},
      doi = {10.11648/j.pamj.s.2015040102.14},
      url = {https://doi.org/10.11648/j.pamj.s.2015040102.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2015040102.14},
      abstract = {In this paper, semi-invariant submanifolds of a generalized Kenmotsu manifold endowed with a semi-symmetric non-metric connection are studied. Necessary and sufficient conditions are given on a submanifold of a generalized Kenmotsu manifold to be semi-invarinat submanifold with semi-symmetric non-metric connection. Morever, we studied the integrability condition of the distribution on semi-invariant submanifolds of generalized Kenmotsu manifold with semi-symmetric non-metric connection.},
     year = {2015}
    }
    

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Author Information
  • Department of Mathematics, Faculty of Arts and Sciences, Gazi University, 06500 Ankara, Turkey

  • Department of Mathematics, Faculty of Arts and Sciences, Gazi University, 06500 Ankara, Turkey

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