The exponential map on the free loop space is fredholm

Geometric and Functional Analysis

Volumn 7, Issue 5, 1997, Pages 954-969

  Misiolłek, Gerard ^a,b  

^a UNIVERSITY OF NOTRE DAME   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031285558     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000390050032     Document Type: Article

References (20)

1. R. ABRAHAM, J. MARSDEN, Foundations of Mechanics, Addison-Wesley 1987.
2. W. BALLMANN, G. THORBERGSSON, W. ZILLER, Closed geodesics on positively curved manifolds, Ann. of Math. 116 (1982), 213-247.
3. J. DOWLING, Finsler geometry on Sobolev manifolds, Proc. Symp. Pure Math. Global Analysis 15 (1970), 1-10.
4. D. EBIN, Espace des metriques Riemanniennes et mouvement des fluides via les varietes d'applications, Ecole Polytechnique, Paris, 1972.
5. D. EBIN, J. MARSDEN, Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of Math. 92 (1970), 102-163.
6. J. EELLS, A setting for global analysis, Bull. A.M.S. 72 (1966), 751-807.
7. H. ELIASSON, Condition (C) and geodesics on Sobolev manifolds, Bull. A.M.S. 77 (1971), 1002-1005.
8. P. FLASCHEL, W. KLINGENBERG, Riemannsche Hilbert-mannigfaltig-keiten, Periodische Geodätische, Springer Lecture Notes in Mathematics 282, New York, 1972.
9. D. FREED, D. GROISSER, The basic geometry of the manifold of Riemannian metrics, Michigan Math. J. 36 (1989), 232-344.
10. I.C. GOHBERG, M. KREIN, The basic propositions on deficiency indices, root numbers and indices of linear operators, Uspiekhi Mat. Nauk 12 (1957), 43-118.
11. D. GROMOLL, W. MEYER, Periodic geodesics on compact riemannian manifolds, J. Diff. Geom. 3 (1969), 493-510.
12. N. GROSSMAN, Hilbert manifolds without epiconjugate points, Proc. A.M.S. 16 (1965), 1365-1371.
13. K. GROVE, Condition (C) for the energy integral on certain path spaces and applications to the theory of geodesics, J. Diff. Geom. 8 (1973), 207-223.
14. 1,M) of closed curves, Comm. Pure Appl. Math. 23 (1970), 201-219.
15. W. KLINGENBERG, Riemannian Geometry, 2nd edition, de Gruyter, Berlin, 1995.
16. S. LANG, Differential and Riemannian Manifolds, Springer, New York, 1995.
17. G. MISIOLŁEK, Stability of flows of ideal fluids and the geometry of the group of diffeomorphisms, Indiana Univ. Math. J. 2 (1993), 215-235.
18. R. PALAIS, Morse theory on Hilbert manifolds, Topology 2 (1963), 299-340.
19. R. PALAIS, Seminar on the Atiyah-Singer index theorem, Ann. of Math. Studies 57 (1965).
20. S. SMALE, An infinite dimensional version of Sard's theorem, Amer. J. Math. 87 (1965), 861-866.