Parallel Translation of Curvature Along Geodesics

DOI10.2307/2000513zbMath0615.53026OpenAlexW4229926422MaRDI QIDQ4722766

James J. Hebda

Publication date: 1987

Full work available at URL: https://doi.org/10.2307/2000513

zbMATH Keywords

curvature tensorisometrybroken geodesicsgeneric metricsCartan-Ambrose-Hicks theorem

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20)

Related Items (7)

Linking curves, sutured manifolds and the Ambrose conjecture for generic 3-manifolds ⋮ Balanced split sets and Hamilton-Jacobi equations ⋮ Cut and singular loci up to codimension 3 ⋮ Extreme points of the distance function on convex surfaces ⋮ Heterogeneous Riemannian manifolds ⋮ Stability of the cut locus and a central limit theorem for Fréchet means of Riemannian manifolds ⋮ The Lipschitz continuity of the distance function to the cut locus

Cites Work

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• The imbedding problem for Riemannian manifolds
• Parallel translation of Riemannian curvature
• The local homology of cut loci in Riemannian manifolds
• Scattering of geodesic fields, I
• Riemannian manifolds in the large
• Cut loci in Riemannian manifolds
• Conjugate loci of constant order
• Connections between differential geometry and topology. II. Closed surfaces
• On Automorphisms of A Kählerian Structure
• Simplicial Structure of the Real Analytic Cut Locus

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