Si descrivono alcuni teoremi sull'esistenza di geodetiche chiuse per varietà di Finsler compatte e semplicemente connesse. Le dimostrazioni appariranno in altri lavori.
@article{RLINA_1976_8_60_2_111_0,
author = {Francesco Mercuri},
title = {Closed geodesics on Finsler manifolds},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
volume = {60},
year = {1976},
pages = {111-117},
zbl = {0362.53052},
mrnumber = {0478085},
language = {en},
url = {http://dml.mathdoc.fr/item/RLINA_1976_8_60_2_111_0}
}
Mercuri, Francesco. Closed geodesics on Finsler manifolds. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 60 (1976) pp. 111-117. http://gdmltest.u-ga.fr/item/RLINA_1976_8_60_2_111_0/
[1] , On periodicity problems in the calculus of variations in the large, «Amer. Math. Soc. Transl.», 14 (2) (1960), 107-172. | MR 113234
[2] and , Foundation of Mechanics, Benjamin, New York and Amsterdam, 1967. | MR 515141
[3] , Seminar on transformation groups, «Ann. of Math. Studies», n. 46, Princeton Unyversity press, Princeton, N.J., 1960. | MR 116341
[4] , The geometry of geodesics, Acad. Press, New York, 1955. | MR 75623 | Zbl 0029.35803
[5] and , On the foundation of calculus of variations, «Ann. of Math.», 49 (1941), 173-198. | MR 3475
[6] , Negligible subsets of infinite dimensional Frechet manifolds, «Proc. Amer. Math. Soc.», 23 (1969), 668-675. | MR 248883
[7] , On the geometry of manifolds of maps, «J. of Diff. Geometry», 1 (1967), 156-194. | MR 226681
[8] , Morse theory for closed curves, Symposium in inf. dim. topology, Ann. of Math. Studies, n. 69, Princeton University Press, Princeton, N. J., 1972, 63-77. | MR 407889
[9] , Variational problems on closed manifolds, «Amer. Math. Soc. Transl.», 90 (1953), 147-206. | MR 56214
[10] and , Periodic geodesics on compact riemannian manifolds, «J. of Diff. Geometry», 3 (1969), 493-510. | MR 264551 | Zbl 0203.54401
[11] , The theorem of the three closed geodesics, «Bull. Amer. Math. Soc.», 71 (1965), 605-610. | MR 177374 | Zbl 0129.35903
[12] , The space of closed curves on the sphere, «Topology», 7 (1968), 395-415. | MR 236957 | Zbl 0174.55102
[13] , Closed geodesics, «Ann. of Math.», 89 (1969), 68-91. | MR 239624 | Zbl 0172.46503
[14] , Lecture on closed geodesics (to appear). | MR 688143 | Zbl 0397.58018
[15] , Closed geodesics on Finsler manifolds, «Doctoral diss.», University of Chicago, 1975. | MR 2611734
[16] , Morse theory, «Ann. Math. Studies», n. 51, Princeton University Press, Princeton, N. J., 1963. | MR 163331
[17] , The calculus of variations in the large, «Amer. Math. Soc. Colloq. Publ.», 18, 1934. | MR 1451874 | Zbl 0011.02802
[18] , Morse theory on Hilbert manifolds, Topology2 (1963), 299-340. | MR 158410 | Zbl 0122.10702
[19] , Liusternik-Schnirelman theory on Banach manifolds, Topology5 (1966), 115-132. | MR 259955 | Zbl 0143.35203
[20] , Foundation of global non-linear analysis, Benjamin, New York, 1968. | MR 248880 | Zbl 0164.11102
[21] and , A generalized Morse theory, «Bull. Amer. Math. Soc.», 70 (1964), 165-172. | MR 158411 | Zbl 0119.09201
[22] , The differential geometry of Finsler spaces, Springer-Verlag, Berlin-Gottingen-Heidelberg, 1959. | MR 105726 | Zbl 0087.36604
[23] , Geometria non euclidea ed ottica geometrica, I, «Rend Acc. Naz. dei Lincei», serie (8) 7 (1949), 16-19. | MR 35503
[24] , Algebraic topology, McGraw Hill, New York, 1966. | MR 210112
[25] , Lecture on differential geometry, Prentice Hall, Englewood Cliffs, N. J., 1964. | MR 193578
[26] , Differential forms and the topology of manifolds, Proceedings of the Japan conference on manifolds, 1973.
[27] and , The homology theory of the closed geodesics problem, Preprint I.H.E.S. | MR 455028
[28] , The conjugate locus of a riemannian manifold, «Amer. J. of Math.», 87 (1965), 575-604. | MR 208534 | Zbl 0129.36002