The present paper deals with weakly symmetric and weakly Ricci symmetric trans-Sasakian manifolds. The existence of weakly Ricci symmetric trans-Sasakian manifolds is ensured by an example.
1. Blair, D. E. Contact manifolds in Riemannian geometry. Lect. Notes Math., 1976, 509.
2. Blair, D. E. and Oubina, J. A. Conformal and related changes of metric on the product of two almost contact metric manifolds. Publ. Math. Debrecen, 1990, 34, 199–207.
3. Chaki, M. C. On pseudosymmetric manifolds. An. Stiint. Univ., “Al. I. Cuza” Iasi, 1987, 33, 53–58.
4. Chaki, M. C. On generalized pseudosymmetric manifolds. Publ. Math. Debrecen, 1994, 45, 305–312.
5. Chaki, M. C. and Koley, S. On generalized pseudo Ricci symmetric manifolds. Periodica Math. Hung., 1994, 28, 123–129.
doi:10.1007/BF01876902
6. De, U. C. and Bandyopadhyay, S. On weakly symmetric Riemannian spaces. Publ. Math. Debrecen, 1999, 54(3–4), 377–381.
7. De, U. C., Binh, T. Q., and Shaikh, A. A. On weakly symmetric and weakly Ricci symmetric K-contact manifolds. Acta Math. Acad. Paedag. Nyíregyház., 2000, 16, 65–71.
8. De, U. C., Shaikh, A. A., and Biswas, S. On weakly Ricci symmetric contact metric manifolds. Tensor N. S., 1994, 28, 123–129.
9. De, U. C. and Tripathi, M. M. Ricci tensor in 3-dimensional trans-Sasakian manifolds. Kyungpook Math. J., 2003, 43(2), 247–255.
10. Kim, J. S., Prasad, R., and Tripathi, M. M. On generalized Ricci-recurrent trans-Sasakian manifolds. J. Korean Math. Soc., 2002, 39(6), 953–961.
11. Oubina, J. A. New class of almost contact metric manifolds. Publ. Math. Debrecen, 1985, 32, 187–193.
12. Özgür, C. On weakly symmetric Kenmotsu manifolds. Diff. Geom. Dynam. Syst., 2006, 8, 204–209.
13. Shaikh, A. A., Baishya, K. K., and Eyasmin, S. On D-homothetic deformation of trans-Sasakian structure. Demonstr. Math., 2008, XLI(1), 171–188.
14. Tamássy, L. and Binh, T. Q. On weakly symmetric and weakly projective symmetric Rimannian manifolds. Coll. Math. Soc., J. Bolyai, 1989, 50, 663–670.
15. Tamássy, L. and Binh, T. Q. On weak symmetries of Einstein and Sasakian manifolds. Tensor N. S., 1993, 53, 140–148.