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Differential geometry: Proc. of the VIII international by Alvarez Lopez J., Garcia-Rio E. (eds.)

By Alvarez Lopez J., Garcia-Rio E. (eds.)

This quantity includes examine and expository papers on fresh advances in foliations and Riemannian geometry. a few of the themes coated during this quantity contain: topology, geometry, dynamics and research of foliations, curvature, submanifold concept, Lie teams and harmonic maps.

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4. B. Deroin, V. Kleptsyn, GAFA vol. 17 (2007) 4 1043-1105. 5. B. Deroin, C. Vernicos, In preparation. 6. J. E. Fornaess, N. Sibony, arXiv:0606744. 7. H. Furstenberg, Amer. J. Math. 83 (1961), 573-601. 8. H. Furstenberg, Ann. of Math. (2) 77 (1963) 477-515. 9. L. Garnett, J. Funct. Anal. 51 (1983) no. 3, 285-311. 10. Y. Guivarc’h, A. Raugi, Z. Wahrsch. Verw. Gebiete 69 (1985), no. 2, 187-242. 11. S. Petite, Erg. Th. Dyn. Syst. 26 (2006), no. 4, 1159-1176. 12. J. Plante, Ann. of Math. 102 (1975), 327-361.

The subgroup G of G generated by g1 and g2 preserves each fiber of the fibration by planes Im(w) R2 → H × R → (0, ∞) , and acts by a discrete lattice of translations on them. Thus the action of G is free and discontinuous, and the quotient G \H × R is a torus bundle over (0, ∞), which is naturally diffeomorphic to T2 × (0, ∞), where T2 is the quotient of R2 by the translations (x, z) → (x + ai , z + bi ), i = 1, 2. The relations g0 ◦ g1 ◦ g0−1 = g1a ◦ g2b and g0 ◦ g2 ◦ g0−1 = g1c ◦ g2d show that the group G is normal in G.

2. P. Baum and J. Cheeger, Topology, 8:173–193, 1969. 3. R. Bott, Michigan Math. , 14:231–244, 1967. February 17, 2009 16:46 WSPC - Proceedings Trim Size: 9in x 6in viii-icdg 34 4. R. Bott, Global Analysis (Proc. Sympos. , Vol. , 1968), Amer. Math. , 1970:127– 131. 5. R. Bott and J. Heitsch, Topology, 11:141-146, 1972. 6. Y. Carri`ere, Comment. Math. Helv. 63:1–20, 1988. 7. J. Cheeger and J. , 1983/84), Lecture Notes in Math. , 1167, Springer, Berlin, 1985: 50–80. 8. S. Chern, Complex manifolds without potential theory, Second Edition.

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