Pacific Journal of Mathematics

Conjugate points on spacelike geodesics or pseudo-selfadjoint Morse-Sturm-Liouville systems.

Adam D. Helfer

Article information

Pacific J. Math., Volume 164, Number 2 (1994), 321-350.

First available in Project Euclid: 8 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)
Secondary: 34B24: Sturm-Liouville theory [See also 34Lxx] 58E10: Applications to the theory of geodesics (problems in one independent variable)


Helfer, Adam D. Conjugate points on spacelike geodesics or pseudo-selfadjoint Morse-Sturm-Liouville systems. Pacific J. Math. 164 (1994), no. 2, 321--350.

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  • [I] J. K. Beem and P. E. Ehrlich, Cut points, conjugatepoints and Lorentzian com- parison theorems, Math. Proc. Cambridge Philos. Soc, 86 (1979), 365-384.
  • [3] J. K. Beem and P. E. Ehrlich, Global Lorentzian Geometry, Marcel Dekker, 1981.
  • [4] R. Bott, The stable homotopy of the classicalgroups,Ann. of Math., 70 (1959), 313-337.
  • [5] N. Dunford and J. T. Schwartz, Linear Operators,Pure and Applied Mathe- matics, volume VII, Wiley Interscience, 1976-71.
  • [6] H. Friedrich, Asymptotic structure of space-time,in Recent advances in general relativity: essays in honor of E. T. Newman, Birkhauser, 1992.
  • [7] I. Gohberg, P. Lancaster and L. Rodman, Matrices and Indefinite Scalar Prod- ucts, Operator Theory: Advances and Applications, vol. 8, Birkhauser (1983).
  • [8] E. L. Ince, Ordinary Differential Equations, Longmans, Green and Co., 1927.
  • [9] P. Libermann and C.-M. Marie, Symplectic Geometry and Analytical Mechanics, D. Reidel, 1987.
  • [10] M. Morse, A generalization of the Sturm separation and comparison theorems in n-space, Math. Ann., 103 (1930), 52-69.
  • [II] M. Morse, The calculus of variations in the large,Amer. Math. Soc. Colloq. PubL, vol. 18, Amer. Math. Soc, Providence, RI, 1934.
  • [12] R. Penrose, Techniquesof differential topologyin relativity, Regional Conference Series in Applied Math., vol. 7, SIAM, Philadelphia, PA, 1972.
  • [13] F. J. Tipler, C. J. S., Clarke and G. F. R. Ellis, Singularities and horizons--a reviewarticle, in General relativity and gravitation: one hundred years after the birth of Albert Einstein, vol. 2, Plenum Press 1980, pp. 97-206.
  • [14] F. Treves, Introduction to Pseudodifferential and FourierIntegral Operators, vol.