Induced volume forms with applications in relativistic kinetic theory
Covariant volume forms are defined in an intrinsic way on a general submanifold of a \(C^{\infty}\) manifold carrying a nondegenerate metric of unspecified signature. The case of covariant volume forms induced on hypersurfaces, null and nonnull, is examined in detail. The results obtained are applied to the various submanifolds of the one-particle phase space of relativistic kinetic theory. Finally a proof of Liouville's theorem is given and its consequences on the Liouville vector are discussed.
scientific article; zbMATH DE number 3899680