Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ON GENERALIZED WEAKLY SEMI-CONFORMALLY SYMMETRIC MANIFOLDS

  • Received : 2020.08.03
  • Accepted : 2021.01.20
  • Published : 2021.10.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we introduce generalized weakly semi-conformally symmetric manifold, a generalization of weakly symmetric manifold. We study some basic properties and obtain the forms of the scalar curvature of such manifold. In the last section an example is given to ensure the existence of such manifold.

Keywords

References

  1. K. K. Baishya, On generalized weakly symmetric manifolds, Bull. Transilv. Univ. Brasov Ser. III 10(59) (2017), no. 1, 31-38.
  2. R. S. D. Dubey, Generalized recurrent spaces, Indian J. Pure Appl. Math. 10 (1979), no. 12, 1508-1513.
  3. S. K. Hui, On weak concircular symmetries of trans-Sasakian manifolds, Cubo 13 (2011), no. 3, 141-152. https://doi.org/10.4067/s0719-06462011000300008
  4. Y. Ishii, On conharmonic transformations, Tensor (N.S.) 7 (1957), 73-80.
  5. S. K. Jana and A. A. Shaikh, On quasi-conformally flat weakly Ricci symmetric manifolds, Acta Math. Hung. 115 (2007), no. 3,197-214; Erratum to: On quasi-conformal flat weakly Ricci symmetric manifolds, Acta Math. Hungarica, 122 (2009), no. 1-2, 201-202. https://doi.org/10.1007/s10474-008-8001-1
  6. J. Kim, A type of conformal curvature tensor, Far East J. Math. Sci. 99 (2016), no. 1, 61-74.
  7. J. Kim, On pseudo semiconformally symmetric manifolds, Bull. Korean Math. Soc. 54 (2017), no. 1, 177-186. https://doi.org/10.4134/BKMS.b151007
  8. A. A. Shaikh and K. K. Baishya, On weakly quasi-conformally symmetric manifolds, Soochow J. Math. 31 (2005), no. 4, 581-595.
  9. A. A. Shaikh and S. K. Hui, On weakly conharmonically symmetric manifolds, Tensor (N.S.) 70 (2008), no. 2, 119-134.
  10. A. A. Shaikh and S. K. Hui, On decomposable weakly conharmonically symmetric manifolds, Lobachevskii J. Math. 29 (2008), no. 4, 206-215. https://doi.org/10.1134/S1995080208040021
  11. A. A. Shaikh and S. K. Hui, On weakly concircular symmetric manifolds, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 55 (2009), no. 1, 167-186.
  12. A. A. Shaikh and S. K. Hui, On weakly projective symmetric manifolds, Acta Math. Acad. Paedagog. Nyhazi. (N.S.) 25 (2009), no. 2, 247-269.
  13. A. A. Shaikh and S. K. Jana, On weakly cyclic Ricci symmetric manifolds, Ann. Polon. Math. 89 (2006), no. 3, 273-288. https://doi.org/10.4064/ap89-3-4
  14. A. A. Shaikh and S. K. Jana, On weakly quasi-conformally symmetric manifolds, SUT J. Math. 43 (2007), no. 1, 61-83.
  15. A. A. Shaikh and S. K. Jana, On weakly symmetric Riemannian manifolds, Publ. Math. Debrecen 71 (2007), no. 1-2, 27-41. https://doi.org/10.5486/PMD.2007.3557
  16. A. A. Shaikh and H. Kundu, On weakly symmetric and weakly Ricci symmetric warped product manifolds, Publ. Math. Debrecen 81 (2012), no. 3-4, 487-505. https://doi.org/10.5486/PMD.2012.5361
  17. A. A. Shaikh and H. Kundu, On equivalency of various geometric structures, J. Geom. 105 (2014), no. 1, 139-165. https://doi.org/10.1007/s00022-013-0200-4
  18. A. A. Shaikh, I. Roy, and S. K. Hui, On totally umbilical hypersurfaces of weakly conharmonically symmetric spaces, Global J. Science Frontier Research 10 (2010), no. 4, 28-31.
  19. A. A. Shaikh, M. H. Shahid, and S. K. Hui, On weakly conformally symmetric manifolds, Mat. Vesnik 60 (2008), no. 4, 269-284.
  20. L. Tamassy and T. Q. Binh, On weakly symmetric and weakly projective symmetric Riemannian manifolds, in Differential geometry and its applications (Eger, 1989), 663-670, Colloq. Math. Soc. Janos Bolyai, 56, North-Holland, Amsterdam, 1992.