Search results for "Pseudo-Riemannian manifold"

showing 2 items of 2 documents

X-ray transforms in pseudo-Riemannian geometry

2016

We study the problem of recovering a function on a pseudo-Riemannian manifold from its integrals over all null geodesics in three geometries: pseudo-Riemannian products of Riemannian manifolds, Minkowski spaces and tori. We give proofs of uniqueness anc characterize non-uniqueness in different settings. Reconstruction is sometimes possible if the signature $(n_1,n_2)$ satisfies $n_1\geq1$ and $n_2\geq2$ or vice versa and always when $n_1,n_2\geq2$. The proofs are based on a Pestov identity adapted to null geodesics (product manifolds) and Fourier analysis (other geometries). The problem in a Minkowski space of any signature is a special case of recovering a function in a Euclidean space fro…

Mathematics - Differential GeometryPure mathematicsGeodesic44A12 53C50 11D09Riemannian geometry01 natural sciencespseudo-Riemannian manifoldsinversio-ongelmatsymbols.namesakeray transformsMathematics - Analysis of PDEsMinkowski spaceFOS: Mathematics0101 mathematicsMathematicsEuclidean space010102 general mathematicsNull (mathematics)Manifold010101 applied mathematicsnull geodesicsDifferential Geometry (math.DG)Differential geometryProduct (mathematics)symbolsGeometry and TopologyMathematics::Differential GeometryAnalysis of PDEs (math.AP)
researchProduct

Feuilletages Riemanniens singuliers

2006

Abstract We prove that a singular foliation on a compact manifold admitting an adapted Riemannian metric for which all leaves are minimal must be regular. To cite this article: V. Miquel, R.A. Wolak, C. R. Acad. Sci. Paris, Ser. I 342 (2006).

Pure mathematicsMathematical analysisGeneral MedicineRiemannian geometryFundamental theorem of Riemannian geometryPseudo-Riemannian manifoldLevi-Civita connectionsymbols.namesakesymbolsMinimal volumeMathematics::Differential GeometryExponential map (Riemannian geometry)Ricci curvatureScalar curvatureMathematicsComptes Rendus Mathematique
researchProduct