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- W4294862305 abstract "The Weyl principle is extended from the Riemannian to the pseudo-Riemannian setting, and subsequently to manifolds equipped with generic symmetric $(0,2)$-tensors. More precisely, we construct a family of generalized curvature measures attached to such manifolds, extending the Riemannian Lipschitz-Killing curvature measures introduced by Federer. We then show that they behave naturally under isometric immersions, in particular they do not depend on the ambient signature. Consequently, we extend Theorema Egregium to surfaces equipped with a generic metric of changing signature, and more generally, establish the existence as distributions of intrinsically defined Lipschitz-Killing curvatures for such manifolds of arbitrary dimension. This includes in particular the scalar curvature and the Chern-Gauss-Bonnet integrand. Finally, we deduce a Chern-Gauss-Bonnet theorem for pseudo-Riemannian manifolds with generic boundary." @default.
- W4294862305 created "2022-09-07" @default.
- W4294862305 creator A5024123562 @default.
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- W4294862305 date "2019-10-21" @default.
- W4294862305 modified "2023-09-29" @default.
- W4294862305 title "Curvature Measures of Pseudo-Riemannian Manifolds" @default.
- W4294862305 doi "https://doi.org/10.48550/arxiv.1910.09635" @default.
- W4294862305 hasPublicationYear "2019" @default.
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