The graph of a totally geodesic foliation

• Autorzy: Robert A. Wolak
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

foliation; totally geodesic; graph

Kategorie tematyczne

• 53C12: Foliations (differential geometric aspects)
• 57R30: Foliations; geometric theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1994-1995
• Tom: 60
• Numer: 3
• Strony: 241-247

Daty

wydano

1995

poprawiono

1993-10-12

Twórcy

autor

Robert A. Wolak

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

Bibliografia

• [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
• [0] 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