Volume Rigidity of Principal Circle Bundles over the Complex Projective Space

TL;DR

This paper proves volume rigidity for principal circle bundles over complex projective space with standard Sasakian structures, under certain positivity conditions related to Tanaka-Webster curvature, contributing to geometric rigidity theory.

Contribution

It establishes volume rigidity results for principal circle bundles over complex projective space with specific curvature conditions, extending understanding of geometric invariants in contact geometry.

Findings

Volume rigidity holds for these bundles under specified curvature conditions.

Rigidity results apply among all K-contact manifolds with positivity conditions.

The work links Sasakian structures, Tanaka-Webster curvature, and volume invariants.

Abstract

In this paper, we prove that principal circle bundles over the complex projective space equipped with the standard Sasakian structures are volume rigid among all $K$-contact manifolds satisfying positivity conditions of tensors involing the Tanaka-Webster curvature.