Communications of the
Korean Mathematical Society CKMS

In the present paper, a Riemannian submersion $\pi$ between Riemannian manifolds such that the total space of $\pi$ endowed with a torse-forming vector field $\nu$ is studied. Some remarkable results of such a submersion whose total space is Ricci soliton are given. Moreover, some characterizations about any fiber of $\pi$ or the base manifold $B$ to be an almost quasi-Einstein are obtained.

Keywords: Ricci soliton, Riemannian submersion, torse-forming vector field

MSC numbers: Primary 53C25, 53C42

Supported by: This work is supported by 1001-Scientific and Technological Research Projects Funding Program of TUBITAK project number 117F434.