On generic submanifolds of LP-Sasakian manifolds with concurrent vector fields
Commun. Korean Math. Soc. 2021 Vol. 36, No. 2, 361-375
Published online September 8, 2020
Printed April 30, 2021
Sujoy Ghosh, Jae-Bok Jun, Avijit Sarkar
Kalyani, Pin-741235, Nadia; Kookmin University; Kalyani, Pin-741235, Nadia
Abstract : The object of the present paper is to deduce some important results on generic submanifolds and also generic product of LP-Sasakian manifolds with concurrent vector fields. Also, we provide a necessary and sufficient condition for which the invariant distribution $D$ and anti-invariant distribution $D^\perp$ of $M$ are Einstein. Also, we deduce an interesting necessary and sufficient condition for submanifolds of LP-Sasakian manifolds to be totally umbilical submanifolds. Especially we deal with the generic submanifolds admitting a Ricci soliton in LP-Sasakian manifolds endowed with concurrent vector fields.
Keywords : LP-Sasakian manifolds, semi-invariant submanifolds, generic semi-invariant submanifolds, totally geodesic submanifolds, totally umbilical submanifolds, concurrent vector fields
MSC numbers : Primary 53C25, 53D15
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