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On the C-Bochner Curvature Tensor of Generalized Sasakian-Space-Forms

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Abstract

In this paper we study C-Bochner pseudosymmetric generalized Sasakian-space-forms and such space-forms with C-Bochner curvature tensor \(B\) satisfying the conditions \(B(\xi , X)\cdot S=0\), \(B(\xi , X)\cdot R=0\) and \(B(\xi , X)\cdot B = 0\), where \(R\) and \(S\) denotes the Riemann curvature tensor and Ricci tensor of the space-form, respectively.

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References

  1. Alegre P, Blair DE, Carriazo A (2004) Generalized Sasakian-space-sorms. Isr J Math 14:157–183

    Article  MathSciNet  Google Scholar 

  2. Alegre P, Carriazo A (2008) Structures on generalized Sasakian-space-forms. Differ Geom Appl 26:656–666

    Article  MATH  MathSciNet  Google Scholar 

  3. Alegre P, Carriazo A (2009) Submanifolds of generalized Sasakian-space-forms. Taiwan J Math 13:923–941

    MATH  MathSciNet  Google Scholar 

  4. De UC, Sarkar A (2010) On the projective curvature tensor of generalized Sasakian-space-forms. Quaest Math 33:245–252

    Article  MATH  MathSciNet  Google Scholar 

  5. Alegre P, Carriazo A (2011) Generalized Sasakian-space-forms and conformal changes of metric. Results Math 59(3–4):485–493

    Article  MATH  MathSciNet  Google Scholar 

  6. Hui SK, Sarkar A (2012) On the \(W_2\)-curvature tensor of generalized Sasakian-space-forms. Math Pannonica 23(1):113–124

    MATH  MathSciNet  Google Scholar 

  7. Kim UK (2006) Conformally flat generalized Sasakian-space-forms and locally symmetric generalized Sasakian-space-forms. Note Math 26:55–67

    MATH  Google Scholar 

  8. Prakasha DG (2012) On generalized Sasakian-space-forms with Weyl-conformal curvature tensor. Lobachevskii J Math 33(3):223–228

    Article  MATH  MathSciNet  Google Scholar 

  9. Upadhyaya A, Gupta RS, Sharfuddin A (2012) Semi-symmetric and Ricci semi-symmetric lightlike hypersurfaces of an indefinite generalized Sasakian-space-form. Int Electron J Geom 5(1):140–150

    MathSciNet  Google Scholar 

  10. Prakasha DG, Nagaraja HG (2013) On quasi-conformally flat and quasi-conformally semisymmetric generalized Sasakian-space-forms. Cubo (Temuco) 15(3):59–70

    Article  MATH  MathSciNet  Google Scholar 

  11. Bochner S (1949) Curvature and Betti numbers. Ann Math 50:77–93

    Article  MATH  MathSciNet  Google Scholar 

  12. Blair DE (1975) On the geometric meaning of the Bochner tensor. Geom Dedicata 4:33–38

    Article  MATH  MathSciNet  Google Scholar 

  13. Boothby WM, Wang HC (1958) On contact manifolds. Ann Math 68:721–734

    Article  MATH  MathSciNet  Google Scholar 

  14. Matsumoto M, Chuman G (1969) On the C-Bochner curvature tensor. TRU Math 5:21–30

    MATH  MathSciNet  Google Scholar 

  15. Blair DE (1976) Contact Manifolds in Riemannian Geometry, vol 509, Lecture Notes in Mathematics. Springer, Berlin

    Google Scholar 

  16. De UC, Samui S (2014) E-Bochner curvature tensor on \((k, \mu )\)-contact metric manifolds. Int Electron J Geom 7(1):143–153

    MATH  MathSciNet  Google Scholar 

  17. Nomizu K (1968) On hypersurfaces satisfying a certain condition on the curvature tensor. Tohoku Math J 20(1):46–59

    Article  MATH  MathSciNet  Google Scholar 

  18. Ogawa YA (1971) Condition for a compact Kahlerian space to be locally symmetric. Nat Sci Rep Ochanomizu Univ 28(1):21–23

    Google Scholar 

  19. Tanno S (1967) Locally symmetric K-contact Riemannian manifold. Proc Jpn Acad 43(7):581–583

    Article  MATH  MathSciNet  Google Scholar 

  20. Szabo ZI (1982) Structure theorems on Riemannian spaces satisfying R(X, Y).R = 0, the local version. J Differ Geom 17:531–582

    MATH  Google Scholar 

  21. Deszcz R (1992) On pseudosymmetric spaces. Bull Soc Math Belg Ser A 44(1):1–34

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Sidho Kanho Birsha University, Purulia, 723101, WB, India

    S. K. Hui

  2. Department of Mathematics, Karnatak University, Dharwad, 580003, India

    D. G. Prakasha

Authors
  1. S. K. Hui
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  2. D. G. Prakasha
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Correspondence to D. G. Prakasha.

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Hui, S.K., Prakasha, D.G. On the C-Bochner Curvature Tensor of Generalized Sasakian-Space-Forms. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 85, 401–405 (2015). https://doi.org/10.1007/s40010-015-0213-5

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  • DOI: https://doi.org/10.1007/s40010-015-0213-5

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