On pseudo-symmetric manifolds admitting a type of semi-symmetric connection. (English) Zbl 0634.53012

Chaki, M. C.; Chaki, B.

Soochow J. Math. 13, No. 1, 1-7 (1987).

The paper is the continuation of two papers by the first author [An. Stiint. Univ. Al. I Cuza Iaşi, N. Ser., Sect. Ia 33, No.1, 53-58 (1987; Zbl 0626.53037) and On pseudo Ricci symmetric manifolds (to appear)], where pseudo-symmetric and pseudo-Ricci symmetric manifolds have been defined. The authors show that a pseudo-symmetric manifold admitting a certain semi-symmetric metric connection is a conformally flat pseudo-Ricci symmetric manifold. Moreover, a simply connected pseudo-symmetric manifold with the same semi-symmetric metric connection can be isometrically immersed as a hypersurface in an Euclidean space.

Reviewer: A.Bucki

MSC:

53B05

Linear and affine connections

Keywords:

subprojective manifold; pseudo-symmetric manifold; pseudo-Ricci symmetric manifold; semi-symmetric metric connection