A note on the Morse index theorem for geodesies between submanifolds in semi-Riemannian geometry

Journal of Mathematical Physics

Volumn 40, Issue 12, 1999, Pages 6682-6688

  Piccione, Paolo ^a   Tausk, Daniel V ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033249112     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.533113     Document Type: Article

References (19)

1. J. K. Beem, P. E. Ehrlich, and K. L. Easley, Global Lorentzian Geometry (Marcel Dekker, New York, 1996).
2. J. Beem and P. Ehrlich, "A Morse Index Theorem for Null Geodesics," Duke Math. J. 46, 561-569 (1979).
3. W. Ambrose, "The Index Theorem in Riemannian Geometry," Ann. Math. 73(1), 49-86 (1961).
4. J. Bolton, "The Morse Index Theorem in the case of Two Variable Endpoints," J. Diff. Geom. 12, 567-581 (1977).
5. D. Kalish, "The Morse Index Theorem where the Ends are Submanifolds," Trans. Am. Math. Soc. 308(1), 341-348 (1988).
6. T. Takahashi, "Correction to The Index Theorem In Riemannian Geometry by W. Ambrose" Ann. Math. 80, 538-541 (1964).
7. N. Hingston and D. Kalish, "The Morse Index Theorem in the Degenerate Endmanifold Case," Proc. Am. Math. Soc. 118(2), 663-668 (1993).
8. P. E. Ehrlich and S. Kim, "A Focal Index Theorem for Null Geodesics," J. Geom. Phys. 6(4), 657-670 (1989).
9. A. D. Helfer, "Conjugate Points on Spacelike Geodesics or Pseudo-Self-Adjoint Morse-Sturm-Liouville Systems," Pac. J. Math. 164(2), 321-340 (1994).
10. H. M. Edwards, "A Generalized Sturm Theorem," Ann. Math. 80, 22-57 (1964).
11. S. Smale, "On the Morse Index Theorem," J. Math. Mech. 14, 1049-1056 (1965).
12. J. Milnor, Morse Theory (Princeton U. P., Princeton, 1969).
13. M. do Carmo, Riemannian Geometry (Birkhäuser, Boston, 1992).
14. S. G. Harris, "A Triangle Comparison Theorem for Lorentz Manifolds," Indiana Univ. Math. J. 31(3), 289-308 (1982).
15. B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity (Academic, New York, 1983).
16. V. Benci, F. Giannoni, and A. Masiello, "Some Properties of the Spectral Flow in Semiriemannian Geometry," J. Geom. Phys. 27, 267-280 (1998).
17. F. Giannoni and P. Piccione, "An Intrinsic Approach to the Geodesical Connectedness of Stationary Lorentzian Manifolds," Commun. An. Geom. 7(1), 157-197 (1999).
18. A. Masiello, Variational Methods in Lorentzian Geometry, Pitman Research Notes in Mathematics Vol. 309 (Longman, London 1994).
19. F. Giannoni, A. Masiello, P. Piccione, and D. Tausk, "A Generalized Index Theorem for Morse-Sturm Systems and Applications to semi-Riemannian Geometry," preprint 1999 (LANL MATH. DG/9908056).