ArticleOriginal scientific text

Title

The graph of a totally geodesic foliation

Authors 1

Affiliations

  1. Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Abstract

We study the properties of the graph of a totally geodesic foliation. We limit our considerations to basic properties of the graph, and from them we derive several interesting corollaries on the structure of leaves.

Keywords

foliation, totally geodesic, graph

Bibliography

  1. R. A. Blumenthal and J. J. Hebda, De Rham decomposition theorem for foliated manifolds, Ann. Inst. Fourier (Grenoble) 33 (1983), 183-198.
  2. R. A. Blumenthal and J. J. Hebda, Complementary distributions which preserve the leaf geometry and applications to totally geodesic foliations, Quart. J. Math. Oxford 35 (1984), 383-392.
  3. R. A. Blumenthal and J. J. Hebda, Ehresmann connections for foliations, Indiana Univ. Math. J. 33 (1984), 597-611.
  4. G. Cairns, Feuilletages géodésiques, thèse, Université du Languedoc, Montpellier, 1987.
  5. G. Hector and U. Hirsch, Introduction to the Geometry of Foliations, Parts A and B, Vieweg, Braunschweig, 1981, 1983.
  6. D. L. Johnson and L. B. Whitt, Totally geodesic foliations, J. Differential Geom. 15 (1980), 225-235.
  7. J. Plante, Foliations with measure preserving holonomy, Ann. of Math. 102 (1975), 327-361.
  8. H. Winkelnkemper, The graph of a foliation, Ann. Global Anal. Geom. 1 (1983), 51-75.
  9. H. Winkelnkemper, The number of ends of the universal leaf of a Riemannian foliation, in: Differential Geometry, Proc., Special Year, Maryland 1981-82, R. Brooks (ed.), Birkhäuser, 1983, 247-254.
  10. R. A. Wolak, Foliations admitting transverse systems of differential equations, Compositio Math. 67 (1988), 89-101.
  11. R. A. Wolak, Le graphe d'un feuilletage admettant un système d'équations différentielles, Math. Z. 201 (1989), 177-182.
  12. R. A. Wolak, Geometric Structures on Foliated Manifolds, Universidad de Santiago de Compostela, 1989
  13. P. Dazord et G. Hector, Intégration symplectique des variétés de Poisson totalement asphériques, in: Symplectic Geometry, Groupoids and Integrable Systems, MSRI Lecture Notes 20, 1991, 37-72
Pages:
241-247
Main language of publication
English
Accepted
1993-10-12
Published
1995
Exact and natural sciences