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On an Almost C(α)-Manifold Satisfying Certain Conditions on the Concircular Curvature Tensor

Received: 10 March 2015     Accepted: 18 March 2015     Published: 11 April 2015
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Abstract

We classify almost C(α)-manifolds, which satisfy the curvature conditions (Z ) ̃(ξ,X)R=0, (Z ) ̃(ξ,X) (Z ) ̃=0, (Z ) ̃(ξ,X)S=0 and (Z ) ̃(ξ,X)P=0, where (Z ) ̃ is the concircular curvature tensor, P is the Weyl projective curvature tensor, S is the Ricci tensor and R is Riemannian curvature tensor of manifold.

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.2015040102.18
Page(s) 31-34
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), 2015. Published by Science Publishing Group

Keywords

Almost C(α)-Manifold, Concircular Curvature Tensor, Projective Curvature Tensor

References
[1] C. Özgür and M. M. Tripathi, On P-Sasakian manifolds satisfying certain conditions on the concircular curvature tensor, Turkish Journal of Math. , 31(2007), 171 – 179.
[2] D. E. Blair, J. S. Kim and M. M. Tripathi, On concircular curvature tensor of a contact metric manifold, J. Korean Math. Soc. 42(2005), 883-892.
[3] D. Janssens and L. Vanhecke, Almost contact structure and curvature tensors, Kodai Math.J., 4(1981), 1-27.
[4] D. Perrone, Contact Riemannian manifolds satisfying R(X, ξ)•R = 0, Yokohama Math. J. 39 (1992), 2, 141-149.
[5] K. Yano and M. Kon, Structures on manifolds, Series in Pure Math., Vol. 3, Word Sci., (1984).
[6] K. Yano, Concircular geometry I. Concircular transformations, Proc. Imp. Acad. Tokyo 16 (1940), 195-200.
[7] M. M. Tripathi and J. S. Kim, On the concircular curvature tensor of a (κ, µ)-manifold, Balkan J. Geom. Appl. 9, no.1, 104 - 114 (2004).
[8] Z. I. Szabo, Structure theorems on Riemannian spaces satisfying R(X, Y).R = 0, the local version, Diff. Geom., 17(1982), 531-582.
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  • APA Style

    Mehmet Atçeken, Umit Yildirim. (2015). On an Almost C(α)-Manifold Satisfying Certain Conditions on the Concircular Curvature Tensor. Pure and Applied Mathematics Journal, 4(1-2), 31-34. https://doi.org/10.11648/j.pamj.s.2015040102.18

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    ACS Style

    Mehmet Atçeken; Umit Yildirim. On an Almost C(α)-Manifold Satisfying Certain Conditions on the Concircular Curvature Tensor. Pure Appl. Math. J. 2015, 4(1-2), 31-34. doi: 10.11648/j.pamj.s.2015040102.18

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    AMA Style

    Mehmet Atçeken, Umit Yildirim. On an Almost C(α)-Manifold Satisfying Certain Conditions on the Concircular Curvature Tensor. Pure Appl Math J. 2015;4(1-2):31-34. doi: 10.11648/j.pamj.s.2015040102.18

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  • @article{10.11648/j.pamj.s.2015040102.18,
      author = {Mehmet Atçeken and Umit Yildirim},
      title = {On an Almost C(α)-Manifold Satisfying Certain Conditions on the Concircular Curvature Tensor},
      journal = {Pure and Applied Mathematics Journal},
      volume = {4},
      number = {1-2},
      pages = {31-34},
      doi = {10.11648/j.pamj.s.2015040102.18},
      url = {https://doi.org/10.11648/j.pamj.s.2015040102.18},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2015040102.18},
      abstract = {We classify almost C(α)-manifolds, which satisfy the curvature conditions (Z ) ̃(ξ,X)R=0, (Z ) ̃(ξ,X) (Z ) ̃=0, (Z ) ̃(ξ,X)S=0 and (Z ) ̃(ξ,X)P=0, where (Z ) ̃ is the concircular curvature tensor, P is the Weyl projective curvature tensor, S is the Ricci tensor and R is Riemannian curvature tensor of manifold.},
     year = {2015}
    }
    

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    T1  - On an Almost C(α)-Manifold Satisfying Certain Conditions on the Concircular Curvature Tensor
    AU  - Mehmet Atçeken
    AU  - Umit Yildirim
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    DO  - 10.11648/j.pamj.s.2015040102.18
    T2  - Pure and Applied Mathematics Journal
    JF  - Pure and Applied Mathematics Journal
    JO  - Pure and Applied Mathematics Journal
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    EP  - 34
    PB  - Science Publishing Group
    SN  - 2326-9812
    UR  - https://doi.org/10.11648/j.pamj.s.2015040102.18
    AB  - We classify almost C(α)-manifolds, which satisfy the curvature conditions (Z ) ̃(ξ,X)R=0, (Z ) ̃(ξ,X) (Z ) ̃=0, (Z ) ̃(ξ,X)S=0 and (Z ) ̃(ξ,X)P=0, where (Z ) ̃ is the concircular curvature tensor, P is the Weyl projective curvature tensor, S is the Ricci tensor and R is Riemannian curvature tensor of manifold.
    VL  - 4
    IS  - 1-2
    ER  - 

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Author Information
  • Gaziosmanpasa University, Faculty of Arts and Sciences, Department of Mathematics, Tokat, Turkey

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