A New Type Warped Product Metric in Contact Geometry

TL;DR

This paper introduces a novel warped product metric in contact geometry, demonstrating an $ ext{α}$-Sasakian structure on certain product manifolds and exploring warped products of almost Hermitian and contact metric manifolds.

Contribution

It proposes a new warped product metric in contact geometry and analyzes its properties on specific product manifolds involving Kaehlerian and almost contact structures.

Findings

Existence of an α-Sasakian structure on the product manifold M₁ × β(I).

Definition of a new warped product metric for almost Hermitian and contact metric manifolds.

Insights into the geometric structure of warped products in contact geometry.

Abstract

In this study, we show that there is an $\alpha$-Sasakian structure on product manifold $M_{1}\times \beta (I)$ where $M_{1}$ is a Kaehlerian manifold that has exact 1-form and $\beta (I)$ is an open curve. After then, we define a new type warped product metric to study the warped product of almost Hermitian manifolds with almost contact metric manifolds.