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Isometric submersions of Finsler manifolds
Author(s):
J.
C.
Álvarez Paiva;
C.
E.
Durán
Journal:
Proc. Amer. Math. Soc.
129
(2001),
2409-2417.
MSC (1991):
Primary 53C22, 53C60;
Secondary 53D20
Posted:
January 17, 2001
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Abstract:
The notion of isometric submersion is extended to Finsler spaces and it is used to construct examples of Finsler metrics on complex and quaternionic projective spaces all of whose geodesics are (geometrical) circles.
References:
-
- 1.
- M. Abate and G. Patrizio, ``Finsler Metrics - A Global Approach", Lecture Notes in Mathematics no. 1591, Springer-Verlag, Berlin, 1994. MR 96b:53087
- 2.
- R. Abraham and J. Marsden, ``Foundations of Mechanics", Benjamin/Cummings, Reading, Mass. 1978. MR 81e:58025
- 3.
- J.C. Álvarez Paiva, Some problems on Finsler geometry, preprint 1999.
- 4.
- J.C. Álvarez Paiva and C. Durán, ``An Introduction to Finsler Geometry", Notas de la Escuela Venezolana de Matématicas, 1998.
- 5.
- J.C. Álvarez Paiva and E. Fernandes, Crofton formulas in projective Finsler spaces, Electronic Research Announcements of the Amer. Math. Soc. 4 (1998), 91-100. MR 99j:53097
- 6.
- J.C. Álvarez Paiva, I.M. Gelfand, and M. Smirnov, Crofton densities, symplectic geometry, and Hilbert's fourth problem, in ``Arnold-Gelfand Mathematical Seminars, Geometry and Singularity Theory", V.I. Arnold, I.M. Gelfand, and V.S. Retakh (eds.), Birkhauser, Boston, 1997, pp. 77-92. MR 98a:52005
- 7.
- H. Busemann, Geometries in which planes minimize area, Ann. Mat. Pura Appl. (4) 55 (1961), 171-190. MR 26:715
- 8.
- W. Klingenberg, ``Riemannian Geometry", de Gruyter, Berlin, New York, 1982. MR 84j:53001
- 9.
- A.V. Pogorelov, ``Hilbert's fourth problem", Scripta Series in Mathematics, Winston and Sons, 1979. MR 80j:53066
- 10.
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- 11.
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Additional Information:
J.
C.
Álvarez Paiva
Affiliation:
Institut de Mathématique Pure et Appliquée, Université Catholique de Louvain, Chemin du Cyclotron 2, B--1348 Louvain--la--Neuve, Belgium
Email:
alvarez@agel.ucl.ac.be
C.
E.
Durán
Affiliation:
IVIC-Matemáticas, Aptdo. 21287, Caracas 1020A, Venezuela
Email:
cduran@cauchy.ivic.ve
DOI:
10.1090/S0002-9939-01-05910-X
PII:
S 0002-9939(01)05910-X
Keywords:
Finsler manifolds,
isometric submersions,
symplectic reduction
Received by editor(s):
December 14, 1999
Posted:
January 17, 2001
Additional Notes:
The first author was partially supported by a {\it Crédit aux Chercheurs} from the FNRS
Dedicated:
Dedicated to Enrique Planchart
Communicated by:
Christopher Croke
Copyright of article:
Copyright
2001,
American Mathematical Society
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