Some Remarks on Riemannian Submersions Admitting An Almost Yamabe Soliton

Year 2020, Volume: 10 Issue: 1, 295 - 306, 25.06.2020

Şemsi Eken Meriç

https://doi.org/10.37094/adyujsci.705319

Abstract

    In this paper, we study the Riemannian submersions $\pi:M\rightarrow B$ whose total manifolds admit an almost Yamabe soliton. Here, we give some necessary conditions for which any fiber of $\pi$ or $B$ are almost Yamabe soliton or Yamabe soliton. Also, we calculate the scalar curvatures of any fiber or $B$ and using them, we present the relations between the scalar curvatures of them and obtain some characterizations of such a soliton (that is, shrinking, steady or expanding).

Keywords

Riemannian manifold, Riemannian submersion, Almost Yamabe soliton

Supporting Institution

TÜBİTAK

Project Number

117F434

Thanks

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

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