On generic submanifold of Sasakian manifold with concurrent vector field

Year 2019, Volume: 68 Issue: 2, 1983 - 1994, 01.08.2019

Halil İbrahim Yoldaş , Şemsi Eken Meriç Erol Yaşar

https://doi.org/10.31801/cfsuasmas.445788

Cited By: 7

Abstract

In the present paper, we deal with the generic submanifold admitting a Ricci soliton in Sasakian manifold endowed with concurrent vector field. Here, we find that there exists never any concurrent vector field on the invariant distribution D of generic submanifold M. Also, we provide a necessary and sufficient condition for which the invariant distribution D and anti-invariant distribution D^{⊥} of M are Einstein. Finally, we give a characterization for a generic submanifold of Sasakian manifold to be a gradient Ricci soliton.

Keywords

Sasakian manifold, Ricci soliton, concurrent vector field

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