Crofton formulas in pseudo-Riemannian space forms

Crofton formulas on simply connected Riemannian space forms allow the volumes, or more generally Lipschitz–Killing curvature integrals of a submanifold with corners, to be computed by integrating Euler characteristic its intersection all geodesic submanifolds. We develop framework distributions replacing measures, which has in core Alesker's Radon transform valuations. then apply this framework, and our recent Hadwiger-type classification, compute explicit for isometry-invariant valuations pseudospheres, pseudo-Euclidean pseudohyperbolic spaces. find that, essence, single measure depends analytically metric, gives rise those through distributional boundary values at parts corresponding different indefinite signatures. In particular, we obtain are formally independent signature.