On the Hofer–Zehnder Capacity of Twisted Tangent Bundles

We calculate the Hofer-Zehnder capacity of the standard and magnetic disk tangent bundles over the real and complex projective space of arbitrary dimension. As a generalization of the complex projective space, we also consider Hermitian symmetric spaces. Here, we provide explicit upper and lower bounds for the Hofer-Zehnder capacity. Furthermore, we describe the relationship between the magnetically twisted symplectic structure below the Mañé's critical value and the hyperkähler structure of a neighborhood of the zero section of the tangent bundle.