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.
Highlights
IntroductionThe ...rst study on semi-invariant submanifold (as a generalization both invariant and anti-invariant submanifolds) of Sasakian manifold was given by Bejancu and Papaghiuc in [5]
The ...rst study on semi-invariant submanifold of Sasakian manifold was given by Bejancu and Papaghiuc in [5]
We deal with the generic submanifold admitting a Ricci soliton in Sasakian manifold endowed with concurrent vector ...eld
Summary
The ...rst study on semi-invariant submanifold (as a generalization both invariant and anti-invariant submanifolds) of Sasakian manifold was given by Bejancu and Papaghiuc in [5]. Perktas and Keles proved that if a 3 dimensional normal almost paracontact metric manifold admits a Ricci soliton, it is shrinking (for details, see [21]). If the potential vector ...eld V is the gradient of a potential function f (i.e., V = rf ), it is called a gradient Ricci soliton. Chen and Deshmukh showed that there do not exist steady or expanding Ricci solitons with concurrent vector ...elds in [9]. We give a characterization for a generic submanifold of Sasakian manifold to be a gradient Ricci soliton
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