Second order parallel tensor in trans-Sasakian manifolds and connection with Ricci soliton
In this paper we have solved the Eisenhart problem for the symmetric case in the trans-Sasakian manifold of type (α, β) with non-vanishing ξ-sectional curvature and studied some of its consequences. Then we apply our result to obtain a Ricci soliton and studied its behavior for a particular case. Finally we studied the possible consequence for an affine Killing vector field.
Keywords and phrasesTrans-sasakianmanifolds parallel second order covariant tensor field, irreducible metric Einstein space Ricci soliton
Unable to display preview. Download preview PDF.
- 8.R. S. Hamilton, Mathematics and general relativity (Santa Cruz, CA, 1986), Contemp. Math. 71, 237 (1988).Google Scholar
- 16.P. Topping, Lectures on the Ricci flow (Cambridge Univ. Press, 2006).Google Scholar
- 17.Mukut Mani Tripathi, Ricci solitons in contact metric manifolds, arXiv:0801.4222v1 [math.DG], 2008.Google Scholar