Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2021; 36(2): 361-375

Online first article September 8, 2020      Printed April 30, 2021

https://doi.org/10.4134/CKMS.c200192

Copyright © The Korean Mathematical Society.

On generic submanifolds of LP-Sasakian manifolds with concurrent vector fields

Sujoy Ghosh, Jae-Bok Jun, Avijit Sarkar

Kalyani, Pin-741235, Nadia; Kookmin University; Kalyani, Pin-741235, Nadia

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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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