On generic submanifold of Sasakian manifold with concurrent vector field

Authors : Halil İbrahim YOLDAŞ, Şemsi EKEN MERİÇ, Erol YAŞAR

Pages : 1983-1994

Doi:10.31801/cfsuasmas.445788

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Publication Date : 2019-08-01

Article Type : Research Paper

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