Some classes of 3-dimensional Trans-Sasakian manifolds with respect to semi-symmetric metric connection | Zendy

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Some classes of 3-dimensional Trans-Sasakian manifolds with respect to semi-symmetric metric connection

Author(s) -

Sampa Pahan

Publication year - 2021

Publication title -

boletim da sociedade paranaense de matemática

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.347

H-Index - 15

eISSN - 2175-1188

pISSN - 0037-8712

DOI - 10.5269/bspm.42855

Subject(s) - connection (principal bundle) , metric connection , manifold (fluid mechanics) , metric (unit) , mathematics , pure mathematics , statistical manifold , field (mathematics) , vector field , mathematical analysis , pseudo riemannian manifold , topology (electrical circuits) , fundamental theorem of riemannian geometry , combinatorics , geometry , information geometry , ricci curvature , mechanical engineering , operations management , curvature , economics , engineering , scalar curvature

The object of the present paper is to study semi-symmetric metric connection on a 3-dimensional trans-Sasakian manifold. We found the necessary condition under which a vector field on a 3-dimensional trans-Sasakian manifold will be a strict contact vector field. Then, we obtained extended generalized phi-recurrent 3-dimensional trans-Sasakian manifold with respect to semi-symmetric metric connection. Next, a 3-dimensional trans-Sasakian manifold satises the condition ~L.~ S = 0 with respect to semi-symmetric metric connection is studied.

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