Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Growth of leaves
in transversely affine foliations


Author: Robert A. Wolak
Journal: Proc. Amer. Math. Soc. 127 (1999), 2167-2173
MSC (1991): Primary 57R30
DOI: https://doi.org/10.1090/S0002-9939-99-04648-1
Published electronically: March 1, 1999
MathSciNet review: 1473682
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this note we give estimates for the growth of leaves in transversely affine foliations which depend on the properties of the affine holonomy group.


References [Enhancements On Off] (What's this?)

  • 1. L. Auslander, L. Green and F. Hahn, Flows on homogeneous spaces, Ann. of Math. Studies, No. 53, 1963. MR 29:4841
  • 2. H. Bass, The degree of polynomial growth of finitely generated nilpotent groups, Proc. London Math. Soc. 25 (1972), 603-614. MR 52:577
  • 3. R. A. Blumenthal, Transversely homogeneous foliations, Ann. Inst. Fourier 29 (1979), 143-158. MR 81h:57011
  • 4. Y. Carrière, Feuilletages riemanniens à croissance polynomiale, Comm. Math. Helv. 63 (1988), 1-20. MR 89a:57033
  • 5. D. B. A. Epstein, K. C. Millet, and D. Tischler, Leaves without holonomy, J. London Math. Soc. 16 (1977), 548-552. MR 57:4193
  • 6. E. Ghys, Flots transvesalement affines et tissus feuilletés, Mém. Soc. Math. France 46 (1991), 123-150. MR 92i:57026
  • 7. E. Ghys and V. Sergiescu, Stabilité et conjugaison différentiable pous certains feuilletages, Topology 19 (1980), 179-197. MR 81k:57022
  • 8. Cl. Godbillon, Feuilletages - Études géométriques, Progress in Math., 98, Birkhäuser, 1991. MR 93i:57038
  • 9. W. Goldman, M. Hirsch, and G. Levitt, Invariant measures for affine foliations, Proc. Amer. Math. Soc. 86 (1982), 511-518. MR 84a:57026
  • 10. A. Haefliger, Pseudogroups of local isometries, Res. Notes in Math., Vol. 131, Pitman, Boston, 1985, 174-197. MR 88i:58174
  • 11. A. Haefliger, Leaf closures in riemannian foliations, A Fète Topology, Academic Press, 1988, 3-32. MR 89c:57033
  • 12. H. Hess, Connections on symplectic manifolds and geometric quantization, Lecture Notes in Math., vol. 836, Springer, 153-165. MR 82j:58056
  • 13. A. I. Malcev, On a class of homogeneous spaces, Izv. Akad. Nauk SSSR Ser. Mat. 13 (1949), 9-32; Amer. Math. Soc. Transl. 9 (1951), 276-301. MR 10:507d; MR 12:589e
  • 14. P. Molino, Feuilletages riemanniens sur les variétés compactes; champs de Killing transverses, C. R. Acad. Sci. Paris 289 (1979), 421-423. MR 80j:57026
  • 15. P. Molino, Riemannian Foliations, Progress in Math., vol. 73, Birkhäuser, 1988. MR 89b:53054
  • 16. P. Molino, Orbit-like foliations, Proc. Geometric Study of Foliations, Tokyo, 1993, (T. Mizutani et al., ed.), World Scientific, 1994, 97-119. MR 97e:57030
  • 17. J. Plante, Foliations with measure preserving holonomy, Ann. of Math. 102 (1975), 327-361. MR 52:11947
  • 18. M. S. Rangunathan, Discrete Subgroups of Lie Groups, Springer, 1972.
  • 19. M.-H. Rigal, Géométrie globale des systemes bihamiltoniens en dimension impaire, Thèse, Montpellier, 1995.
  • 20. I. Vaisman, $d_f$-cohomology of Lagrangian foliations, Mh. Math. 106 (1988), 221-244. MR 89m:58084
  • 21. R. A. Wolak, On $\nabla-G$-foliations, Rend. Cir. Mat. Palermo (2) 1984 Suppl. No. 6, 329-341. MR 86f:53038
  • 22. R. A. Wolak, Foliated and associated geometric structures on foliated manifolds, Ann. Fac. Sci. Toulouse Math. 10 (1989), 337-360. MR 97g:53036
  • 23. R. A. Wolak, Transversely affine foliations compared with affine manifolds, Quart. J. Math. Oxford 41 (1990), 369-384. MR 91g:57031
  • 24. R. A. Wolak, Closures of leaves in transversely affine foliations, Canad. Math. Bull. 34 (1991), 553-558. MR 93f:53022

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 57R30

Retrieve articles in all journals with MSC (1991): 57R30


Additional Information

Robert A. Wolak
Affiliation: Instytut Matematyki, Uniwersytet Jagielloński, Wl. Reymonta 4, 30-059 Kraków, Poland
Email: wolak@im.uj.edu.pl

DOI: https://doi.org/10.1090/S0002-9939-99-04648-1
Keywords: Transversely affine foliations, leaves, growth
Received by editor(s): March 27, 1997
Received by editor(s) in revised form: July 30, 1997
Published electronically: March 1, 1999
Communicated by: Christopher Croke
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society