Infinitesimal conjugacies and Weil-Petersson metric
Fathi, Albert ; Flaminio, L.
Annales de l'Institut Fourier, Tome 43 (1993), p. 279-299 / Harvested from Numdam
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Nous étudions les déformations de variétés riemanniennes compactes à courbure strictement négative. Nous établissons une équation pour la conjugaison infinitésimale entre les flots géodésiques, ce qui nous permet de donner des dérivées de l’intersection de métriques. Nous obtenons une nouvelle démonstration d’un théorème de Wolpert.

We study deformations of compact Riemannian manifolds of negative curvature. We give an equation for the infinitesimal conjugacy between geodesic flows. This in turn allows us to compute derivatives of intersection of metrics. As a consequence we obtain a proof of a theorem of Wolpert.

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     author = {Fathi, Albert and Flaminio, L.},
     title = {Infinitesimal conjugacies and Weil-Petersson metric},
     journal = {Annales de l'Institut Fourier},
     volume = {43},
     year = {1993},
     pages = {279-299},
     doi = {10.5802/aif.1331},
     mrnumber = {94c:58149},
     zbl = {0769.58005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1993__43_1_279_0}
}

Fathi, Albert; Flaminio, L. Infinitesimal conjugacies and Weil-Petersson metric. Annales de l'Institut Fourier, Tome 43 (1993) pp. 279-299. doi : 10.5802/aif.1331. http://gdmltest.u-ga.fr/item/AIF_1993__43_1_279_0/

[An] D. Anosov, Geodesic flows on closed Riemannian manifolds with negative sectional curvature, english translation, Proc. Steklov Inst. Math., 90 (1967). | MR 36 #7157 | Zbl 0176.19101

[Bo] F. Bonahon, Bouts de variétés hyperboliques de dimension 3, Ann. of Math., 124 (1986), 71-158. | MR 88c:57013 | Zbl 0671.57008

[CF] C. Croke & A. Fathi, An inequality between energy and intersection, Bull. London Math. Soc., 22 (1990), 489-494. | MR 92d:58042 | Zbl 0719.53020

[FT] A. Fischer & A. Tromba, On a purely Riemmanian proof of the structure and dimension of the unramified moduli space of a compact Riemann surface, Math. Ann., 267 (1984), 311-345. | MR 85m:58045 | Zbl 0518.32015

[Gh] E. Ghys, Flots d'Anosov sur les 3-variétés fibrées en cercles, Ergodic Theory Dynamical Systems, 4 (1984), 67-80. | MR 86b:58098 | Zbl 0527.58030

[Gr] M. Gromov, Three remarks on the geodesic flow, preprint.

[GK] V. Guillemin & D. Kazhdan, Some inverse spectral results for negatively curved 2-manifolds, Topology, 19 (1980), 301-312. | MR 81j:58082 | Zbl 0465.58027

[Kl] W. Klingenberg, Riemannian Geometry, Walter de Gruyter, Berlin, New York, 1982. | MR 84j:53001 | Zbl 0495.53036

[LM] R. De La Llave & R. Moriyon, Invariants for smooth conjugacy of hyperbolic dynamical systems IV, Commun. Math. Phys., 116-4 (1988), 185-192. | MR 90h:58064 | Zbl 0673.58038

[LMM] R. De La Llave, J. M. Marco & R. Moriyon, Canonical perturbation theory of Anosov systems and regularity results for Livsic cohomology equation, Ann. of Math., 123 (1986), 537-611. | MR 88h:58091 | Zbl 0603.58016

[La] S. Lang, SL2 (R), Graduate Texts in Mathematics 105, Springer-Verlag, Heidelberg, New York & Tokyo, 1985. | Zbl 0583.22001

[Mo] M. Morse, A fundamental class of geodesics on any closed surface of genus greater than one, Trans. Amer. Math. Soc., 26 (1924), 25-60. | JFM 50.0466.04

[Ta] M. Taylor, Noncommutative harmonic analysis, Providence, American Mathematical Society, 1986. | MR 88a:22021 | Zbl 0604.43001

[Tr] A. Tromba, A classical variational approach to Teichmüller theory in “Topics in calculus of variations”, ed. M. Giaquinta, Springer Lecture Notes in Mathematics, 1365, 155-185. | MR 91a:32029 | Zbl 0694.49030

[Wo] S. Wolpert, Thurston's Riemannian metric for Teichmüller space, J. Differential Geom., 23 (1986), 143-174. | MR 88c:32035 | Zbl 0592.53037