arXiv research

New superintegrable systems derived from Frobenius structures.

Two Kaehler metrics on one complex manifold are said to be c-projectively equivalent if their J-planar curves, i.e., curves defined by the property that their acceleration is complex proportional to their velocity, coincide. The degree of mobility of a Kaehler metric is the dimension of the space of metrics that are c-…

Given a Kähler manifold $M$ endowed with a Hamiltonian Killing vector field $Z$, we construct a conical Kähler manifold $\hat{M}$ such that $M$ is recovered as a Kähler quotient of $\hat{M}$. Similarly, given a hyper-Kähler manifold $(M,g,J_1,J_2,J_3)$ endowed with a Killing vector field $Z$, Hamiltonian with respect t…