Open AccessSome classes of 3-dimensional Trans-Sasakian manifolds with respect to semi-symmetric metric connection
Author(s) -
Sampa Pahan
Publication year - 2022
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 , field (mathematics) , mathematical analysis , vector field , statistical manifold , 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.