Growth of leaves in transversely affine foliations

Wolak, Robert

doi:10.1090/S0002-9939-99-04648-1

Growth of leaves in transversely affine foliations
HTML articles powered by AMS MathViewer

by Robert A. Wolak PDF

Proc. Amer. Math. Soc. 127 (1999), 2167-2173 Request permission

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

L. Auslander, L. Green, and F. Hahn, Flows on homogeneous spaces, Annals of Mathematics Studies, No. 53, Princeton University Press, Princeton, N.J., 1963. With the assistance of L. Markus and W. Massey, and an appendix by L. Greenberg. MR 0167569, DOI 10.1515/9781400882021
H. Bass, The degree of polynomial growth of finitely generated nilpotent groups, Proc. London Math. Soc. (3) 25 (1972), 603–614. MR 379672, DOI 10.1112/plms/s3-25.4.603
Robert A. Blumenthal, Transversely homogeneous foliations, Ann. Inst. Fourier (Grenoble) 29 (1979), no. 4, vii, 143–158 (English, with French summary). MR 558593
Yves Carrière, Feuilletages riemanniens à croissance polynômiale, Comment. Math. Helv. 63 (1988), no. 1, 1–20 (French). MR 928025, DOI 10.1007/BF02566750
D. B. A. Epstein, K. C. Millett, and D. Tischler, Leaves without holonomy, J. London Math. Soc. (2) 16 (1977), no. 3, 548–552. MR 464259, DOI 10.1112/jlms/s2-16.3.548
Étienne Ghys, Flots transversalement affines et tissus feuilletés, Mém. Soc. Math. France (N.S.) 46 (1991), 123–150 (French). Analyse globale et physique mathématique (Lyon, 1989). MR 1125840
E. Ghys and V. Sergiescu, Stabilité et conjugaison différentiable pour certains feuilletages, Topology 19 (1980), no. 2, 179–197 (French). MR 572582, DOI 10.1016/0040-9383(80)90005-1
Claude Godbillon, Feuilletages, Progress in Mathematics, vol. 98, Birkhäuser Verlag, Basel, 1991 (French). Études géométriques. [Geometric studies]; With a preface by G. Reeb. MR 1120547
William M. Goldman, Morris W. Hirsch, and Gilbert Levitt, Invariant measures for affine foliations, Proc. Amer. Math. Soc. 86 (1982), no. 3, 511–518. MR 671227, DOI 10.1090/S0002-9939-1982-0671227-8
A. Haefliger, Pseudogroups of local isometries, Differential geometry (Santiago de Compostela, 1984) Res. Notes in Math., vol. 131, Pitman, Boston, MA, 1985, pp. 174–197. MR 864868
André Haefliger, Leaf closures in Riemannian foliations, A fête of topology, Academic Press, Boston, MA, 1988, pp. 3–32. MR 928394
Harald Hess, Connections on symplectic manifolds and geometric quantization, Differential geometrical methods in mathematical physics (Proc. Conf., Aix-en-Provence/Salamanca, 1979) Lecture Notes in Math., vol. 836, Springer, Berlin, 1980, pp. 153–166. MR 607691
Morgan Ward, Ring homomorphisms which are also lattice homomorphisms, Amer. J. Math. 61 (1939), 783–787. MR 10, DOI 10.2307/2371336
Pierre Molino, Feuilletages riemanniens sur les variétés compactes; champs de Killing transverses, C. R. Acad. Sci. Paris Sér. A-B 289 (1979), no. 7, A421–A423 (French, with English summary). MR 554633
Pierre Molino, Riemannian foliations, Progress in Mathematics, vol. 73, Birkhäuser Boston, Inc., Boston, MA, 1988. Translated from the French by Grant Cairns; With appendices by Cairns, Y. Carrière, É. Ghys, E. Salem and V. Sergiescu. MR 932463, DOI 10.1007/978-1-4684-8670-4
Pierre Molino, Orbit-like foliations, Geometric study of foliations (Tokyo, 1993) World Sci. Publ., River Edge, NJ, 1994, pp. 97–119. MR 1363720
J. F. Plante, Foliations with measure preserving holonomy, Ann. of Math. (2) 102 (1975), no. 2, 327–361. MR 391125, DOI 10.2307/1971034
M. S. Rangunathan, Discrete Subgroups of Lie Groups, Springer, 1972.
M.-H. Rigal, Géométrie globale des systemes bihamiltoniens en dimension impaire, Thèse, Montpellier, 1995.
Izu Vaisman, $d_f$-cohomology of Lagrangian foliations, Monatsh. Math. 106 (1988), no. 3, 221–244. MR 971925, DOI 10.1007/BF01318683
Robert A. Wolak, On $\nabla$-$G$-foliations, Proceedings of the 12th winter school on abstract analysis (Srní, 1984), 1984, pp. 329–341. MR 782729, DOI 10.1007/BF02568481
Robert A. Wolak, Foliated and associated geometric structures on foliated manifolds, Ann. Fac. Sci. Toulouse Math. (5) 10 (1989), no. 3, 337–360 (English, with English and French summaries). MR 1425491, DOI 10.5802/afst.681
Robert A. Wolak, Transversely affine foliations compared with affine manifolds, Quart. J. Math. Oxford Ser. (2) 41 (1990), no. 163, 369–384. MR 1067491, DOI 10.1093/qmath/41.3.369
Robert A. Wolak, Closure of leaves in transversely affine foliations, Canad. Math. Bull. 34 (1991), no. 4, 553–558. MR 1136659, DOI 10.4153/CMB-1991-087-8