Infinitesimal conjugacies and Weil-Petersson metric
Annales de l'Institut Fourier, Tome 43 (1993) no. 1, pp. 279-299.

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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     title = {Infinitesimal conjugacies and {Weil-Petersson} metric},
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Fathi, Albert; Flaminio, L. Infinitesimal conjugacies and Weil-Petersson metric. Annales de l'Institut Fourier, Tome 43 (1993) no. 1, pp. 279-299. doi : 10.5802/aif.1331. http://www.numdam.org/articles/10.5802/aif.1331/

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

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

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

[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 | Zbl

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

[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 | Zbl

[Kl] W. Klingenberg, Riemannian Geometry, Walter de Gruyter, Berlin, New York, 1982. | MR | Zbl

[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 | Zbl

[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 | Zbl

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

[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

[Ta] M. Taylor, Noncommutative harmonic analysis, Providence, American Mathematical Society, 1986. | MR | Zbl

[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 | Zbl

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

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