Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지
DOI QR코드

DOI QR Code

On Almost Pseudo Conharmonically Symmetric Manifolds

  • Pal, Prajjwal (Chakdaha Co-operative Colony Vidyayatan (H. S.))
  • Received : 2012.10.30
  • Accepted : 2013.03.14
  • Published : 2014.12.23
Download PDF
⟨ Previous Next ⟩

Abstract

The object of the present paper is to study almost pseudo conharmonically symmetric manifolds. Some geometric properties of almost pseudo conharmonically symmetric manifolds have been studied under certain curvature conditions. Finally, we give three examples of almost pseudo conharmonically symmetric manifolds.

Keywords

References

  1. Abdussattar, D. B. and Dwivedi, B., On conharmonic transformation in general relativity, Bull. Cal. Math. Soc., 6(1996), 465-470.
  2. Adati, T. and Miyazawa, T., On a Riemannian space with recurrent conformal curvature, Tensor(N.S.), 18(1967), 348-354.
  3. Ahsan, Z., Tensor Analysis with Applications, Anamaya Publishers, New Delhi, India, (2008).
  4. Binh, T. Q., On weakly symmetric Riemannian spaces, Publ. Math. Debrecen, 42(1993), 103-107.
  5. Cartan, E., Sur une classes remarquable d'espaces de Riemannian, Bull. Soc. Math. France, 54(1926), 214-264.
  6. Chaki, M. C. and Gupta, B., On conformally symmetric spaces, Indian J. Math., 5(1963), 113-122.
  7. Chaki, M. C., On pseudo symmetric manifolds, Ann. St. Univ. "Al I Cuza" Iasi, 33(1987), 53-58.
  8. De, U. C. and Bandyopadhyay, S., On weakly symmetric spaces, Publ. Math. Debrecen, 54(1999), 377-381.
  9. De, U. C. and Bandyopadhyay, S., On weakly symmetric spaces, Acta Math. Hungarica, 83(3)(2000), 205-212.
  10. De, U. C. and Gazi, A. K., On almost pseudo symmetric manifolds, Annales Univ. Sci. Budapest., 51(2008), 53-68.
  11. De, U. C. and Gazi, A. K., On almost pseudo conformally symmetric manifolds, Demonstratio Mathematica, 4(2009), 869-886.
  12. De, U. C. and Gazi, A. K., On conformally flat almost pseudo Ricci symmetric manifolds, Kyungpook Math. J., 49(2009), 507-520. https://doi.org/10.5666/KMJ.2009.49.3.507
  13. De, U. C. and De, Avik, On almost pseudo-conformally symmetric Ricci-recurrent manifolds with applications to relativity, Czechoslovak Math. J., 62(2012), 1055-1072. https://doi.org/10.1007/s10587-012-0063-0
  14. De, U. C. and Mallick, Sahanous, On almost pseudo concircularly symmetric manifolds, The Journal of Mathematics and Computer Science, 4(2012), 317-330.
  15. Deszcz, R. and Grycak, W., On some class of wraped product manifolds, Bull. Inst. Math. Acad. Sinica, 19(1987), 311-322.
  16. Gray, A., Einstein-like manifolds which are not Einstein, Geom. Dedicata, 7(1978), 259-280.
  17. Ishii, Y. , On conharmonic transformation in general relativity, The Tensor Society. Tensor. New Series, 7(1957), 73-80.
  18. O'Neill, B., Semi-Riemannian Geometry with Applications to the Relativity, Academic Press, New York-London, 1983.
  19. Ozgur, C., On ${\phi}$-conformally flat Lorentzian para-Sasakian manifolds, Radovi Matematicki, 12(2003), 99-106.
  20. Prvanovic, M., On weakly symmetric Riemannian manifolds, Publ. Math. Debrecen, 46(1995), 19-25.
  21. Prvanovic, M., On totally umbilical submanifolds immersed in a weakly symmetric Riemannian manifold, Yzves. Vuz. Matematika(Kazan), 6(1998), 54-64.
  22. Roter, W., On conformally symmetric Ricci-recurrent spaces, Colloquium Mathematicum., 31(1974), 87-96. https://doi.org/10.4064/cm-31-1-87-96
  23. Siddiqui, S. A. and Ahsan. Z., Conharmonic curvature tensor and the space time of general relativity, Differential Geometry-Dynamical Systems, 12(2010), 213-220.
  24. Tamassy, L. and Binh, T. Q., On weakly symmetric and weakly projectively symmetric Riemannian manifolds, Colloq. Math. Soc. Janos Bolyai , 56(1989), 663-670.
  25. Walker, A. G., On Ruse's space of recurrent curvature, Proc. of London Math. Soc., 52(1950), 36-54.