Abstract
The object of the present work is to obtain a necessary condition for the existence of weakly symmetric and weakly Ricci-symmetric Sasakian manifolds admitting a quarter-symmetric metric connection.
Similar content being viewed by others
References
Nirmala S. Agashe and Mangala R. Chafle, A semi-symmetric non-metric connection on a Riemannian Manifold, Indian J. Pure Appl. Math., 23 (1992), 399–409.
D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math. No. 509, Springer (1976).
A. De, On almost pseudo-symmetric manifolds admitting a semi-symmetric non-metric connection, Acta Math. Hungar., 125 (2009), 183–186.
U. C. De and A. K. Gazi, On almost pseudo-symmetric manifolds, to appear in Ann. Univ. Sci. Budapest. Eötvös, Sect. Math.
S. Golab, On semi-symmetric and quarter-symmetric linear connections, Tensor (N.S.), 29 (1975), 249–254.
H. A. Hayden, Subspaces of a space with torsion, Proc. London Math. Soc., 34 (1932), 27–50.
R. S. Mishra and S. N. Pandey, On quarter-symmetric metric F-connections, Tensor (N.S.), 34 (1980), 1–7.
A. K. Mondal and U. C. De, Some properties of a quarter-symmetric metric connection on a Sasakian manifold, Bull. Math. Analysis Appl., 1 (2009), 99–108.
S. C. Rastogi, On quarter-symmetric metric connection, C.R. Acad. Sci. Bulgar, 31 (1978), 811–814.
S. C. Rastogi, On quarter-symmetric metric connection, Tensor (N.S.), 44 (1987), 133–141.
S. Sasaki, Lectures Notes on Almost Contact Manifolds, Part I, Tohoku University (1975).
S. Sular, Some properties of a Kenmotsu manifold with a semi-symmetric metric connection, International Electronic Journal of Geometry, 3 (2010), 24–34.
L. Tamássy and T. Q. Binh, On weakly symmetric and weakly projective symmetric Riemannian manifolds, Colloq. Math. Soc. J. Bolyai, 56 (1992), 663–670.
L. Tamássy and T. Q. Binh, On weak symmetries of Einstein and Sasakian manifolds, Tensor (N.S.), 53 (1993), 140–148.
K. Yano, On semi-symmetric connection, Rev. Roumaine Math., Pure Appl. Math., 15 (1970), 1579–1586.
K. Yano and T. Imai, Quarter-symmetric metric connections and their curvature tensors, Tensor (N.S.), 38 (1982), 13–18.
K. Yano and M. Kon, Structures on Manifolds, Series in Pure Mathematics, 3, World Scientific Publishing Co. (Singapore, 1984).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jaiswal, J.P. The existence of weakly symmetric and weakly Ricci-symmetric Sasakian manifolds admitting a quarter-symmetric metric connection. Acta Math Hung 132, 358–366 (2011). https://doi.org/10.1007/s10474-011-0076-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10474-011-0076-4
Key words and phrases
- quarter-symmetric metric connection
- Sasakian manifold
- weakly symmetric manifold
- weakly Ricci-symmetric manifold