Mercuri, Francesco:
Closed geodesics on Finsler manifolds
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Serie 8 60 (1976), fasc. n.2, p. 111-117, (English)
pdf (646 Kb), djvu (1.01 MB). | MR 0478085 | Zbl 0362.53052
Sunto
Si descrivono alcuni teoremi sull'esistenza di geodetiche chiuse per varietà di Finsler compatte e semplicemente connesse. Le dimostrazioni appariranno in altri lavori.
Referenze Bibliografiche
[1]
S. I. ALBER,
On periodicity problems in the calculus of variations in the large, «
Amer. Math. Soc. Transl.»,
14 (2) (
1960), 107-172. |
MR 113234[2]
R. ABRAHAM and
J. MARSDEN,
Foundation of Mechanics,
Benjamin, New York and Amsterdam,
1967. |
MR 515141[3]
A. BOREL,
Seminar on transformation groups, «
Ann. of Math. Studies», n.
46,
Princeton Unyversity press, Princeton, N.J.,
1960. |
MR 116341[5]
H. BUSEMAN and
W. MAYER,
On the foundation of calculus of variations, «
Ann. of Math.»,
49 (
1941), 173-198. |
fulltext (doi) |
MR 3475[6]
W. H. CULTER,
Negligible subsets of infinite dimensional Frechet manifolds, «
Proc. Amer. Math. Soc.»,
23 (
1969), 668-675. |
fulltext (doi) |
MR 248883[7]
H. ELLIASON,
On the geometry of manifolds of maps, «
J. of Diff. Geometry»,
1 (
1967), 156-194. |
MR 226681[8]
H. ELLIASON,
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]
A. I. FET,
Variational problems on closed manifolds, «
Amer. Math. Soc. Transl.»,
90 (
1953), 147-206. |
MR 56214[10]
D. GROMOLL and
W. MEYER,
Periodic geodesics on compact riemannian manifolds, «
J. of Diff. Geometry»,
3 (
1969), 493-510. |
MR 264551 |
Zbl 0203.54401[15]
F. MERCURI,
Closed geodesics on Finsler manifolds, «Doctoral diss.», University of Chicago,
1975. |
MR 2611734[16]
J. MILNOR,
Morse theory, «
Ann. Math. Studies», n.
51,
Princeton University Press, Princeton, N. J.,
1963. |
MR 163331[17]
M. MORSE,
The calculus of variations in the large, «
Amer. Math. Soc. Colloq. Publ.»,
18,
1934. |
MR 1451874 |
Zbl 0011.02802[22]
H. RUND,
The differential geometry of Finsler spaces,
Springer-Verlag, Berlin-Gottingen-Heidelberg,
1959. |
MR 105726 |
Zbl 0087.36604[23]
B. SEGRE,
Geometria non euclidea ed ottica geometrica, I, «
Rend Acc. Naz. dei Lincei», serie (8)
7 (
1949), 16-19. |
MR 35503[24]
E. SPANIER,
Algebraic topology,
McGraw Hill, New York,
1966. |
MR 210112[25]
S. STEMBERG,
Lecture on differential geometry,
Prentice Hall, Englewood Cliffs, N. J.,
1964. |
MR 193578[26] S. SULLIVAN, Differential forms and the topology of manifolds, Proceedings of the Japan conference on manifolds, 1973.
[27]
D. SULLIVAN and
M. VIGUE-PORRIER,
The homology theory of the closed geodesics problem, Preprint I.H.E.S. |
MR 455028