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Conjugate points in
Author(s):
Gerard
Misiolek
Journal:
Proc. Amer. Math. Soc.
124
(1996),
977-982.
MSC (1991):
Primary 58B20, 58D05;
Secondary 76E99
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Abstract:
An example of a geodesic in with conjugate points is given, thus providing an affirmative answer to a question of V.I. Arnol d.
References:
- [A]
- V. I. Arnol
d, Sur la geometrie differentielle des groupes de Lie de dimension infinie et ses applications a l'hydrodynamique des fluids parfaits, Ann. Inst. Grenoble 16 (1966).MR 34:1956 - [CE]
- J. Cheeger and D. Ebin, Comparison theorems in Riemannian geometry, North-Holland, New York, 1975.MR 56:16538
- [DFGHMS]
- T. Dombre, U. Frisch, J. M. Greene, M. Henon, A. Mehr, and A. M. Soward, Chaotic streamlines in the ABC flows, J. Fluid Mech. 167 (1986).
- [EM]
- D. Ebin and J. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of Math. (2) 92 (1970).MR 42:6865
- [FGV]
- S. Friedlander, A. Gilbert, and M. Vishik, Hydrodynamic instability for certain ABC flows, preprint.
- [G]
- N. Grossman, Hilbert manifolds without epiconjugate points, Proc. Amer. Math. Soc. 16 (1965).MR 32:6370
- [M]
- G. Misio{\l}ek, Stability of flows of ideal fluids and the geometry of the group of diffeomorphisms, Indiana Univ. Math. J. 42 (1993). MR 94j:58027
- [Y]
- K. Yosida, Functional analysis, 6th ed., Springer-Verlag, New York, 1980.
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Additional Information:
Gerard
Misiolek
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email:
misiolek.1@nd.edu
DOI:
10.1090/S0002-9939-96-03149-8
PII:
S 0002-9939(96)03149-8
Keywords:
Conjugate points,
diffeomorphism groups
Received by editor(s):
January 24, 1994
Received by editor(s) in revised form:
September 16, 1994
Communicated by:
Barbara Lee Keyfitz
Copyright of article:
Copyright
1996,
American Mathematical Society
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