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
DOI:
https://doi.org/10.1090/S1079-6762-98-00053-5
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 $\mathbb {R}^n$ 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
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 credit aux chercheurs from the FNRS
Communicated by:
Dmitri Burago
Article copyright:
© Copyright 1998
American Mathematical Society