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On weakly semiconformally symmetric manifolds

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Abstract

The object of the present paper is to study weakly semiconformally symmetric manifolds (WSCS)n. At first some geometric properties of (WSCS)n (n > 2) have been studied. Finally, we consider the decomposability of (WSCS)n.

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References

  1. Binh, T.Q.: On weakly symmetric Riemannian spaces. Publ. Math. Debrecen 42, 103–107 (1993)

    MathSciNet  MATH  Google Scholar 

  2. Chaki, M.C.: On pseudo symmetric manifolds. Ann. St. Univ. ``Al I Cuza'' Iasi 33, 53–58 (1987)

    MathSciNet  MATH  Google Scholar 

  3. Chern, S.S.: What is geometry? Amer. Math. Monthly 97, 679–686 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  4. De, U.C.: On weakly symmetric structures on Riemannian manifolds, Facta Univ. Ser. Mech. Automat. Control Robot. 3, 805–819 (2003)

    MathSciNet  Google Scholar 

  5. De, U.C.: On weakly conformally symmetric Ricci-recurrent spaces. Publ. Math. Debrecen 62, 379–386 (2003)

    MathSciNet  MATH  Google Scholar 

  6. De, U.C., Bandyopadhyay, S.: On weakly symmetric spaces. Publ. Math. Debrecen 54, 377–381 (1999)

    MathSciNet  MATH  Google Scholar 

  7. De, U.C., Bandyopadhyay, S.: On weakly symmetric spaces. Acta Math. Hungar. 83, 205–212 (2000)

    MathSciNet  MATH  Google Scholar 

  8. De, U.C., Mallick, S.: On weakly symmetric spacetimes. Kragujevac J. Math. 36, 299–308 (2012)

    MathSciNet  MATH  Google Scholar 

  9. De, U.C., Mantica, A.C., Molinari, L.G., Suh, Y.J.: On weakly cyclic Z-symmetric spacetimes. Acta Math. Hungar. 149, 462–477 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  10. De, U.C., Mantica, A.C., Suh, Y.J.: On weakly cyclic Z-symmetric manifolds. Acta Math. Hungar. 146, 153–167 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  11. De, U.C., Sengupta, J.: On a weakly symmetric Riemannian manifold admitting a special type of semi-symmetric metric connection. Novi Sad. J. Math. 29, 89–95 (1999)

    MathSciNet  MATH  Google Scholar 

  12. Gray, A.: Einstein-like manifolds which are not Einstein. Geom. Dedicata 7, 259–280 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kim, J.: On pseudo semiconformally symmetric manifolds. Bull. Korean Math. Soc. 54, 177–186 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  14. J. Kim, A type of conformal curvature tensor, Far East J. Math. Soc., to appear

  15. Kim, J.: Notes on weakly cyclic Z-symmetric manifolds. Bull. Korean Math. Soc. 55, 227–237 (2018)

    MathSciNet  MATH  Google Scholar 

  16. Mantica, A.C., Molinari, L.G.: Weakly Z-symmetric manifolds. Acta Math. Hungar. 135, 80–96 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  17. Mantica, A.C., Molinari, L.G.: A second-order identity for the Riemannian tensor and applications. Colloq. Math. 122, 69–82 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. A. C. Mantica and Y. J. Suh, Pseudo Z-symmetric Riemannian manifolds with harmonic curvature tensors, Int. J. Geom. Meth. Mod. Phys., 9 (2012) 1250004, 21 pp

  19. Ozen, F., Altay, S.: Weakly and pseudo-symmetric Riemannian spaces. Indian J. Pure Appl. Math. 33, 1477–1488 (2002)

    MathSciNet  MATH  Google Scholar 

  20. F. Ozen and S. Altay, On weakly and pseudo-concircular symmetric structures on a Riemannian manifold, Acta Univ. Palack. Olomuc., Fac. Rerum. Natur. Math., 47 (2008) 129–138

  21. Prvanović, M.: On weakly symmetric Riemannian manifolds. Publ. Math. Debrecen 46, 19–25 (1995)

    MathSciNet  MATH  Google Scholar 

  22. Schouten, J.A.: Ricci-Calculus. Springer-Verlag (Berlin-Göttingen-Heidelberg, An introduction to Tensor Analysis and its Geometrical Applications (1954)

    Book  MATH  Google Scholar 

  23. Sen, R.N., Chaki, M.C.: On curvature restrictions of a certain kind of conformally flat Riemannian space of class one. Proc. Nat. Inst. Sci. India 33, 100–102 (1967)

    MathSciNet  MATH  Google Scholar 

  24. Shaikh A.A., Hui S.K.: On weakly conharmonically symmetric manifolds. Tensor (N.S.), 70, 119–134 (2008)

    MathSciNet  MATH  Google Scholar 

  25. Tamássy, L., Binh, T.Q.: On weakly symmetric and weakly projectively symmetric Riemannian manifolds. Colloq. Math. Soc. János Bolyai 56, 663–670 (1989)

    MATH  Google Scholar 

  26. Tamássy L., Binh T.Q.: On weak symmetries of Einstein and Sasakian manifolds. Tensor (N. S.), 53, 140–148 (1993)

    MathSciNet  MATH  Google Scholar 

  27. Yano K., Kon M.: Structures on Manifolds. World Scientific, Singapore (1984)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata, 700019, West Bengal, India

    U. C. De

  2. Department of Mathematics and RIRCM, Kyungpook National University, Taegu, 702-701, South Korea

    Y. J. Suh

Authors
  1. U. C. De
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  2. Y. J. Suh
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Correspondence to U. C. De.

Additional information

The second author is supported by Grant Proj. No. NRF-2018- R1D1A1B-05040381 from National Research Foundation of Korea

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De, U.C., Suh, Y.J. On weakly semiconformally symmetric manifolds. Acta Math. Hungar. 157, 503–521 (2019). https://doi.org/10.1007/s10474-018-0879-7

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  • DOI: https://doi.org/10.1007/s10474-018-0879-7

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