Geodesic
Crofton formulas in projective Finsler spaces
Álvarez Paiva, J.1 ; Fernandes, E.1
1 Université Catholique de Louvain, Institut de Mathématique Pure et Appl., Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve, Belgium
Electronic research announcements of the American Mathematical Society, Tome 04 (1998), pp. 91-100.

Voir la notice de l'article provenant de la source American Mathematical Society

We extend the classical Crofton formulas in Euclidean integral geometry to Finsler metrics on $\mathbb {R}^n$ whose geodesics are straight lines.
DOI : 10.1090/S1079-6762-98-00053-5

Álvarez Paiva, J. 1 ; Fernandes, E. 1

1 Université Catholique de Louvain, Institut de Mathématique Pure et Appl., Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve, Belgium 
@article{ERAAMS_1998_04_a12,
     author = {\'Alvarez Paiva, J. and Fernandes, E.},
     title = {Crofton formulas in projective {Finsler} spaces},
     journal = {Electronic research announcements of the American Mathematical Society},
     pages = {91--100},
     publisher = {mathdoc},
     volume = {04},
     year = {1998},
     doi = {10.1090/S1079-6762-98-00053-5},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-98-00053-5/}
}
TY  - JOUR
AU  - Álvarez Paiva, J.
AU  - Fernandes, E.
TI  - Crofton formulas in projective Finsler spaces
JO  - Electronic research announcements of the American Mathematical Society
PY  - 1998
SP  - 91
EP  - 100
VL  - 04
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-98-00053-5/
DO  - 10.1090/S1079-6762-98-00053-5
ID  - ERAAMS_1998_04_a12
ER  - 
%0 Journal Article
%A Álvarez Paiva, J.
%A Fernandes, E.
%T Crofton formulas in projective Finsler spaces
%J Electronic research announcements of the American Mathematical Society
%D 1998
%P 91-100
%V 04
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-98-00053-5/
%R 10.1090/S1079-6762-98-00053-5
%F ERAAMS_1998_04_a12
Álvarez Paiva, J.; Fernandes, E. Crofton formulas in projective Finsler spaces. Electronic research announcements of the American Mathematical Society, Tome 04 (1998), pp. 91-100. doi : 10.1090/S1079-6762-98-00053-5. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-98-00053-5/

[1] Alvarez, J. C., Gelfand, I. M., Smirnov, M. Crofton densities, symplectic geometry and Hilbert’s fourth problem 1997 77 92

[2] Arnol′D, V. I., Givental′, A. B. Symplectic geometry 1985

[3] Besse, Arthur L. Manifolds all of whose geodesics are closed 1978

[4] Busemann, Herbert Problem IV: Desarguesian spaces 1976 131 141

[5] Busemann, Herbert Areas in affine spaces. III. The integral geometry of affine area Rend. Circ. Mat. Palermo (2) 1960 226 242

[6] Busemann, Herbert Geometries in which the planes minimize area Ann. Mat. Pura Appl. (4) 1961 171 189

[7] Gelfand, Israel M., Smirnov, Mikhail M. Lagrangians satisfying Crofton formulas, Radon transforms, and nonlocal differentials Adv. Math. 1994 188 227

[8] Mathematical developments arising from Hilbert problems 1976

[9] Holmes, R. D., Thompson, A. C. 𝑛-dimensional area and content in Minkowski spaces Pacific J. Math. 1979 77 110

[10] Pogorelov, Aleksei Vasil′Evich Hilbert’s fourth problem 1979

[11] Schneider, Rolf, Wieacker, John André Integral geometry in Minkowski spaces Adv. Math. 1997 222 260

[12] Szabó, Z. I. Hilbert’s fourth problem. I Adv. in Math. 1986 185 301

[13] Thompson, A. C. Minkowski geometry 1996

Cité par Sources :