On an almost complex manifold, a quasi-Kähler metric, with canonical connection in the c-projective class of given minimal connection, is equivalent to nondegenerate solution c-projectively invariant metrizability equation. For this overdetermined equation, replacing maximal rank condition on solutions nondegeneracy prolonged system yields strictly wider non-vanishing (generalized) scalar curva...

We show an analogue of the Lorentzian splitting theorem for weighted Lorentz-Finsler manifolds: If a Berwald spacetime nonnegative Ricci curvature satisfies certain completeness and metrizability conditions includes timelike straight line, then it necessarily admits one-dimensional family isometric translations generated by gradient vector field Busemann function. Moreover, our formulation in t...

When $G$ is a Polish group, metrizability of the universal minimal flow has been shown to be robust dividing line in complexity topological dynamics $G$. We introduce class groups, CAP which provides neat generalization this all groups. prove number characterizations class, having very different flavors, and use these that groups enjoys nice closure properties. As concrete application, we compu...