On a generalized quarter symmetric metric recurrent connection

Abstract

We introduce a generalized quarter-symmetric metric recurrent connection and study its geometrical properties. We also derive the Schur's theorem for the generalized quarter-symmetric metric recurrent connection.

Geometries of manifolds equipped with a Ricci (projection-Ricci) quarter-symmetric connection

“…where k is a scalar curvature of the the Levi-Civita connection. Using this expression, from the expressions (23) and (24), we have…”

“…In [10,17], a projective(projective-like) invariant of a quarter-symmetric metric connections was obtained. Afterwards, some properties of several types of a quarter-symmetric metric connection were studied ( [7,11,20,[23][24][25][27][28][29][30][31]). Recently, Han, Fu and Zhao [12,13] studied similar problems in Sub-Riemannian manifolds.…”

On a Ricci quarter-symmetric metric recurrent connection and a projective Ricci quarter-symmetric metric recurrent connection in a Riemannian manifold

“…In [7,14,20,23,24], the geometric and physic properties of conformal and projective the semi-symmetric metric recurrent connections were studied. And in [17,18] a projective conformal quarter-symmetric metric connection and a generalized quarter-symmetric metric recurrent connection were studied. In [5] a curvature copy problem of the symmetric connection was studied.…”

On a projective conformal semi-symmetric connection

“…K.Yano in [21] introduced firstly and investigated a semi-symmetric metric connection, and T. Imai in [15] studied its properties. Afterwards some kinds of semi-symmetric connections were studied in [10,20,24]. A semi-symmetric connection that is projectively equivalent to the Levi-Civita connection was defined as a projective semi-symmetric connection and some of its properties were investigated ( [22,23]).…”