Riemannian Submersions Whose Total Space is Endowed with a Torse-Forming Vector Field
Commun. Korean Math. Soc. Published online May 13, 2022
Semsi Eken Meric and Erol Kılıç
Mersin University; İnönü University
Abstract : 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 : Riemannian Submersion, Ricci Soliton, Torse-Forming Vector Field