Some semisymmetry conditions on Riemannian manifolds (Q2815307)

The authors study a Riemannian manifold \((M,g)\) admitting a semisymmetric metric connection determined by the distinguished vector field \(U\), such that \(U\) is a parallel unit vector field with respect to the Levi-Civita connection. They show that that if \(M\) is projectively flat with respect to the semisymmetric metric connection, then \(M\) is a quasi-Einstein manifold. They also give a characterization of manifolds \(M\) which are also projectively semisymmetric, and sufficient condition for manifold \(M\) to be conformally flat quasi-Einstein in the case when the dimension of \(M\) is greater than three.