Hofer-Zehnder capacity of disc tangent bundles of projective spaces

TL;DR

This paper calculates the Hofer-Zehnder capacity of disc tangent bundles of complex and real projective spaces, providing explicit bounds and extending results to magnetically twisted cases with various twists.

Contribution

It offers explicit computations and bounds for the Hofer-Zehnder capacity of tangent bundles of projective spaces, including twisted cases, advancing symplectic capacity understanding.

Findings

Explicit capacity values for complex and real projective spaces

Bounds for various metrics and twists

Extension to magnetically twisted tangent bundles

Abstract

We compute the Hofer-Zehnder capacity of disc tangent bundles of the complex and real projective spaces of any dimension. The disc bundle is taken with respect to the Fubini-Study resp. round metric, but we can obtain explicit bounds for any other metric. In the case of the complex projective space we also compute the Hofer-Zehnder capacity for the magnetically twisted case, where the twist is proportional to the Fubini-Study form. For arbitrary twists we can still give explicit upper bounds.