IJPAM: Volume 87, No. 3 (2013)

ON 3-DIMENSIONAL ($\epsilon$,$\delta$)-TRANS-SASAKIAN STRUCTURE

Y.B. Maralabhavi$^1$, G.S. Shivaprasanna$^2$, G. Somashekhara$^3$
$^{1,2,3}$Department of Mathematics
Central College Campus
Bangalore University
Bengaluru, 560 001, Karnataka, INDIA


Abstract. The object of present paper is to study 3-dimensional $(\varepsilon,\delta)$-trans-Sasakian manifold admitting Ricci solitons and $K$-torse forming vector fields. We prove the conditions for the Ricci solitons to be shrinking, expanding and steady. Further, we have obtained a condition for the vector field $\xi$ in a generalized recurrent 3-dimensional $(\varepsilon,\delta)$-trans-Sasakian manifold to be co-symplectic. We have also shown that such a manifold $M$ is of constant scalar curvature.

Received: April 13, 2013

AMS Subject Classification: 53D10, 53D15

Key Words and Phrases: ( $\epsilon,\delta$)trans-Sasakian manifold, Ricci soliton, shrinking, steady, expanding, K-torseforming vector field

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DOI: 10.12732/ijpam.v87i3.4 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 87
Issue: 3