On the cut loci of a von Mangoldt's surface of revolution

DOI10.2969/jmsj/04440631zbMath0789.53023OpenAlexW2057687829MaRDI QIDQ1801840

Minoru Tanaka

Publication date: 17 August 1993

Published in: Journal of the Mathematical Society of Japan (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2969/jmsj/04440631

zbMATH Keywords

cut locussurfaces of revolutionrotationally symmetriccomplete Riemannian metrics

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20)

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Loki: Software for Computing Cut Loci ⋮ The Set of Poles of a Two-Sheeted Hyperboloid ⋮ Geodesic flow of the averaged controlled Kepler equation ⋮ The cut loci, conjugate loci and poles in a complete Riemannian manifold ⋮ A new family of latitudinally corrugated two-spheres of revolution with simple cut locus structure ⋮ Generalized von Mangoldt surfaces of revolution and asymmetric two-spheres of revolution with simple cut locus structure ⋮ Cut loci and conjugate loci on Liouville surfaces ⋮ Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. I ⋮ Remarks on the set of poles on a pointed complete surface ⋮ Euclidean position in Euclidean 2-orbifolds. ⋮ The Alexandrov-Toponogov comparison theorem for radial curvature ⋮ A sphere theorem for radial curvature ⋮ Toponogov comparison theorem for open triangles ⋮ On average curvatures of convex curves in surfaces ⋮ Radius sphere theorems for compact manifolds with radial curvature bounded below ⋮ The cut locus of a two-sphere of revolution and Toponogov's comparison theorem ⋮ Comparison geometry referred to warped product models ⋮ Local estimate on convexity radius and decay of injectivity radius in a Riemannian manifold ⋮ Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. II ⋮ Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. III ⋮ Necessary and sufficient conditions for a triangle comparison theorem ⋮ A Bound on the Number of Endpoints of the Cut Locus

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