Second order parallel tensor in trans-Sasakian manifolds and connection with Ricci soliton
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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
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