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The local homology of cut loci in Riemannian manifolds. (English) Zbl 0512.53041


MSC:

53C20 Global Riemannian geometry, including pinching
53C22 Geodesics in global differential geometry
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References:

[1] A. BESSE, Manifolds all of whose geodesies are closed, Springer-Verlag, Berlin, Heidelberg, and New York, 1979. · Zbl 0387.53010
[2] R. BISHOP, Decomposition of cut loci, Proc. Amer. Math. Soc. 65 (1976), 133-136 · Zbl 0373.53019 · doi:10.2307/2042008
[3] M. BUCHNER, Simplicial structure of the real analytic cut locus, Proc. Amer. Math. Soc 66 (1977), 118-121. JSTOR: · Zbl 0373.53020 · doi:10.2307/2040994
[4] M. BUCHNER, The structure of the cut locus in dimension less than or equal to six, Compositio Math. 37 (1978), 103-119. · Zbl 0407.58008
[5] B. -Y. CHEN, Geometry of submanifolds, Marcel Decker, New York, 1973 · Zbl 0262.53036
[6] A. DOLD, Lectures on algebraic topology, Springer-Verlag, Berlin, Heidelberg, and Ne York, 1972. · Zbl 0234.55001
[7] H. GLUCK AND D. SINGER, Scattering of geodesic fields, I, Ann. of Math. 108 (1978), 347-372. JSTOR: · Zbl 0399.58011 · doi:10.2307/1971170
[8] J. HEBDA, Conjugate and cut loci and the Cartan-Ambrose-Hicks Theorem, Indiana U. Math. J. 31 (1982), 17-25. · Zbl 0485.53040 · doi:10.1512/iumj.1982.31.31003
[9] W. HUREWICZ AND H. WALLMAN, Dimension Theory, Princeton University Press, Prin ceton, 1941. Zentralblatt MATH: · Zbl 0060.39808
[10] S. KOBAYASHI, On conjugate and cut loci, Studies in Global Geometry and Analysi (S. S. Chern, ed.), MAA Studies in Mathematics (1967), 96-122. · Zbl 0683.53043
[11] S. B. MYERS, Connections between differential geometry and topology I and II, Duk Math. J. 1 (1935), 376-391, ibid. 2 (1936), 95-102. Zentralblatt MATH: · Zbl 0012.27502 · doi:10.1215/S0012-7094-35-00126-0
[12] V. OZOLS, Cut loci in Riemannian manifolds, Thoku Math. J. 26 (1974), 219-227 · Zbl 0285.53034 · doi:10.2748/tmj/1178241180
[13] F. W. WARNER, The conjugate locus of a Riemannian manifold, Amer. J. Math. 8 (1965), 575-604. JSTOR: · Zbl 0129.36002 · doi:10.2307/2373064
[14] F. W. WARNER, Conjugate loci of constant order, Ann. of Math. 86 (1967), 192-212 JSTOR: · Zbl 0172.23003 · doi:10.2307/1970366
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