Non Existence of 𝒫𝑅-semi-slant Warped Product Submanifolds in a Para-Kähler Manifold

Anil Sharma

doi:10.5666/KMJ.2020.60.1.197

Article

Kyungpook Mathematical Journal 2020; 60(1): 197-210

Published online March 31, 2020

Non Existence of 𝒫𝑅-semi-slant Warped Product Submanifolds in a Para-Kähler Manifold

Anil Sharma

Chitkara University Institute of Engineering and Technology, Chitkara University, Punjab, India
e-mail : sharma.anil@chitkara.edu.in
Department of Mathematics, Symbiosis Institute of Technology, Symbiosis International University, Pune 412115, India
e-mail : anilsharma3091991@gmail.com

Received: December 26, 2018; Revised: January 7, 2020; Accepted: January 16, 2020

Abstract

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Abstract

In this paper, we prove that there are no non-trivial ℘ℛ-semi-slant warped product submanifolds with proper slant coefficients in para-Kähler manifolds M̄. We also present a numerical example that illustrates the existence of a ℘ℛ-warped product submanifold in M̄.

Keywords: slant submanifold, warped product, para-Ka¨hler manifold, pseudoRiemannian manifold.