Browse > Article
http://dx.doi.org/10.4134/CKMS.c200278

ON GENERALIZED WEAKLY SEMI-CONFORMALLY SYMMETRIC MANIFOLDS  

Hui, Shyamal Kumar (Department of Mathematics The University of Burdwan)
Patra, Akshoy (Department of Mathematics The University of Burdwan)
Patra, Ananta (Department of Mathematics Kandi Raj College)
Publication Information
Communications of the Korean Mathematical Society / v.36, no.4, 2021 , pp. 771-782 More about this Journal
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
Weakly symmetric manifold; generalized weakly symmetric manifold; semi-conformal curvature tensor; generalized weakly conformally symmetric manifold;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Y. Ishii, On conharmonic transformations, Tensor (N.S.) 7 (1957), 73-80.
2 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   DOI
3 J. Kim, A type of conformal curvature tensor, Far East J. Math. Sci. 99 (2016), no. 1, 61-74.
4 J. Kim, On pseudo semiconformally symmetric manifolds, Bull. Korean Math. Soc. 54 (2017), no. 1, 177-186. https://doi.org/10.4134/BKMS.b151007   DOI
5 A. A. Shaikh and K. K. Baishya, On weakly quasi-conformally symmetric manifolds, Soochow J. Math. 31 (2005), no. 4, 581-595.
6 A. A. Shaikh and S. K. Hui, On weakly conharmonically symmetric manifolds, Tensor (N.S.) 70 (2008), no. 2, 119-134.
7 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.
8 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.
9 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   DOI
10 A. A. Shaikh and S. K. Jana, On weakly quasi-conformally symmetric manifolds, SUT J. Math. 43 (2007), no. 1, 61-83.
11 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   DOI
12 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   DOI
13 K. K. Baishya, On generalized weakly symmetric manifolds, Bull. Transilv. Univ. Brasov Ser. III 10(59) (2017), no. 1, 31-38.
14 R. S. D. Dubey, Generalized recurrent spaces, Indian J. Pure Appl. Math. 10 (1979), no. 12, 1508-1513.
15 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   DOI
16 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   DOI
17 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.
18 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.
19 A. A. Shaikh and S. K. Jana, On weakly symmetric Riemannian manifolds, Publ. Math. Debrecen 71 (2007), no. 1-2, 27-41.   DOI
20 A. A. Shaikh, M. H. Shahid, and S. K. Hui, On weakly conformally symmetric manifolds, Mat. Vesnik 60 (2008), no. 4, 269-284.