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Crofton formulas in projective Finsler spaces
Author(s):
J.
C.
Álvarez Paiva;
E.
Fernandes
Journal:
Electron. Res. Announc. Amer. Math. Soc.
4
(1998),
91-100.
MSC (1991):
Primary 53C65;
Secondary 53C60
Posted:
November 23, 1998
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Abstract:
We extend the classical Crofton formulas in Euclidean integral geometry to Finsler metrics on  whose geodesics are straight lines.
References:
- 1.
- J.C. Álvarez Paiva, Integral geometry on Finsler manifolds, preprint 1998.
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- 3.
- 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.), Birkhäuser, Boston, 1997, pp. 77-92. MR 98a:52005
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Additional Information:
J.
C.
Álvarez Paiva
Affiliation:
Université Catholique de Louvain, Institut de Mathématique Pure et Appl., Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve, Belgium
Email:
alvarez@agel.ucl.ac.be
E.
Fernandes
Affiliation:
Université Catholique de Louvain, Institut de Mathématique Pure et Appl., Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve, Belgium
Email:
fernandes@agel.ucl.ac.be
DOI:
10.1090/S1079-6762-98-00053-5
PII:
S 1079-6762(98)00053-5
Keywords:
Crofton formulas,
Hilbert's fourth problem,
Finsler geometry
Received by editor(s):
August 08, 1998
Posted:
November 23, 1998
Additional Notes:
Partially supported by a credit aux chercheurs from the FNRS
Communicated by:
Dmitri Burago
Copyright of article:
Copyright
1998,
American Mathematical Society
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