Tohoku Mathematical Journal

The local homology of cut loci in Riemannian manifolds

James J. Hebda

Full-text: Open access

Article information

Source
Tohoku Math. J. (2) Volume 35, Number 1 (1983), 45-52.

Dates
First available: 3 May 2007

Permanent link to this document
http://projecteuclid.org/euclid.tmj/1178229100

Mathematical Reviews number (MathSciNet)
MR0695658

Zentralblatt MATH identifier
0512.53041

Digital Object Identifier
doi:10.2748/tmj/1178229100

Subjects
Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]
Secondary: 57R99: None of the above, but in this section

Citation

Hebda, James J. The local homology of cut loci in Riemannian manifolds. Tohoku Mathematical Journal 35 (1983), no. 1, 45--52. doi:10.2748/tmj/1178229100. http://projecteuclid.org/euclid.tmj/1178229100.


Export citation

References

  • [1] A. BESSE, Manifolds all of whose geodesies are closed, Springer-Verlag, Berlin, Heidelberg, and New York, 1979.
  • [2] R. BISHOP, Decomposition of cut loci, Proc. Amer. Math. Soc. 65 (1976), 133-136
  • [3] M. BUCHNER, Simplicial structure of the real analytic cut locus, Proc. Amer. Math. Soc 66 (1977), 118-121.
  • [4] M. BUCHNER, The structure of the cut locus in dimension less than or equal to six, Compositio Math. 37 (1978), 103-119.
  • [5] B. -Y. CHEN, Geometry of submanifolds, Marcel Decker, New York, 1973
  • [6] A. DOLD, Lectures on algebraic topology, Springer-Verlag, Berlin, Heidelberg, and Ne York, 1972.
  • [7] H. GLUCK AND D. SINGER, Scattering of geodesic fields, I, Ann. of Math. 108 (1978), 347-372.
  • [8] J. HEBDA, Conjugate and cut loci and the Cartan-Ambrose-Hicks Theorem, Indiana U. Math. J. 31 (1982), 17-25.
  • [9] W. HUREWICZ AND H. WALLMAN, Dimension Theory, Princeton University Press, Prin ceton, 1941.
  • [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.
  • [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.
  • [12] V. OZOLS, Cut loci in Riemannian manifolds, Thoku Math. J. 26 (1974), 219-227
  • [13] F. W. WARNER, The conjugate locus of a Riemannian manifold, Amer. J. Math. 8 (1965), 575-604.
  • [14] F. W. WARNER, Conjugate loci of constant order, Ann. of Math. 86 (1967), 192-212