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ISSN 1079-6762

Crofton formulas in projective Finsler spaces


Authors: J. C. Álvarez Paiva and E. Fernandes
Journal: Electron. Res. Announc. Amer. Math. Soc. 4 (1998), 91-100
MSC (1991): Primary 53C65; Secondary 53C60
Published electronically: November 23, 1998
MathSciNet review: 1655987
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Abstract: We extend the classical Crofton formulas in Euclidean integral geometry to Finsler metrics on ${\Bbb R}^n$ whose geodesics are straight lines.


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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: http://dx.doi.org/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 8, 1998
Published electronically: November 23, 1998
Additional Notes: Partially supported by a \itshape credit aux chercheurs from the FNRS
Communicated by: Dmitri Burago
Article copyright: © Copyright 1998 American Mathematical Society