A Note on Doubly Warped Product Contact CR-Submanifolds in trans-Sasakian Manifolds

Abstract

Warped product CR-submanifolds in Kaehlerian manifolds were intensively studied only since 2001 after the impulse given by B.Y. Chen. Immediately after, another line of research, similar to that concerning Sasakian geometry as the odd dimensional version of Kaehlerian geometry, was developed, namely warped product contact CR-submanifolds in Sasakian manifolds. In this note we proved that there exists no proper doubly warped product contact CR-submanifolds in trans-Sasakian manifolds.

arXiv comment5 Latex pages

Cited by in corpus (5)

• On warped product submanifolds of Kenmotsu manifolds
• Geometry of $\mathcal{PR}$-semi-invariant warped product submanifolds in paracosymplectic manifold
• Pseudo parallel contact CR-Submanifolds of Kenmotsu manifolds
• Doubly Warped Product Finsler Manifolds with Some Non-Riemannian Curvature Properties
• Warped Product Conformal Kahler Manifolds and Kenmotsu Structures