The length of a cut locus on a surface and ambrose’s problem

Journal of Differential Geometry

Volumn 43, Issue 3, 1996, Pages 642-651

  Itoh, Jin Ichi ^a  

^a KUMAMOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000576031     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1214458326     Document Type: Article

References (10)

1. W. Ambrose, Parallel translation of Riemannian curvature, Ann. of Math. 64 (1956) 337-363.
2. J. Cheeger & D. Ebin, Comparison theorems in Riemannian geometry, North-Holland, Amsterdam, 1975.
3. H. Gluck & D. Singer, Scattering of geodesic fields, I, Ann. of Math. 108 (1978) 347-372.
4. P. Hartman, Geodesic parallel coordinates in the large, Amer. J. Math. 86 (1964) 705-727.
5. J. Hebda, Parallel translation of curvature along geodesies, Trans. Amer. Math. Soc. 299 (1987) 559-572.
6. J. Hebda, Metric structure of cut loci in surfaces and Ambrose's problem, J. Differential Geom. 40 (1994) 621-642.
7. J. Itoh, C1 ' 1 metric with fractal cut locus, Preprint.
8. H. Poincare, Sur les linges geodesiques des surfaces convexes, Trans. Amer. Math. Soc. 6 (1905) 237-274.
9. [91 S. B. Myers, Connections between differential geometry and topoloqy. J, Duke Math. J. 1 (1935) 376-391.
10. K. Shiohama & M. Tanaka, Cut loci and distance spheres on Alexsandrov surfaces, Preprint.