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Lobachevskii Journal of Mathematics

, Volume 33, Issue 4, pp 312–316 | Cite as

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

Article

Abstract

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 phrases

Trans-sasakianmanifolds parallel second order covariant tensor field, irreducible metric Einstein space Ricci soliton 

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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Department of MathematicsJadavpur UniversityKolkataIndia

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