The graph of a totally geodesic foliation

Robert A. Wolak

Annales Polonici Mathematici (1995)

  • Volume: 60, Issue: 3, page 241-247
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Robert A. Wolak. "The graph of a totally geodesic foliation." Annales Polonici Mathematici 60.3 (1995): 241-247. <http://eudml.org/doc/262505>.

@article{RobertA1995,
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.},
author = {Robert A. Wolak},
journal = {Annales Polonici Mathematici},
keywords = {foliation; totally geodesic; graph; totally geodesic foliation},
language = {eng},
number = {3},
pages = {241-247},
title = {The graph of a totally geodesic foliation},
url = {http://eudml.org/doc/262505},
volume = {60},
year = {1995},
}

TY - JOUR
AU - Robert A. Wolak
TI - The graph of a totally geodesic foliation
JO - Annales Polonici Mathematici
PY - 1995
VL - 60
IS - 3
SP - 241
EP - 247
AB - 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.
LA - eng
KW - foliation; totally geodesic; graph; totally geodesic foliation
UR - http://eudml.org/doc/262505
ER -

References

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  1. [1] R. A. Blumenthal and J. J. Hebda, De Rham decomposition theorem for foliated manifolds, Ann. Inst. Fourier (Grenoble) 33 (1983), 183-198. Zbl0487.57010
  2. [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. Zbl0572.57016
  3. [3] R. A. Blumenthal and J. J. Hebda, Ehresmann connections for foliations, Indiana Univ. Math. J. 33 (1984), 597-611. Zbl0511.57021
  4. [4] G. Cairns, Feuilletages géodésiques, thèse, Université du Languedoc, Montpellier, 1987. 
  5. [5] G. Hector and U. Hirsch, Introduction to the Geometry of Foliations, Parts A and B, Vieweg, Braunschweig, 1981, 1983. Zbl0486.57002
  6. [6] D. L. Johnson and L. B. Whitt, Totally geodesic foliations, J. Differential Geom. 15 (1980), 225-235. Zbl0444.57017
  7. [7] J. Plante, Foliations with measure preserving holonomy, Ann. of Math. 102 (1975), 327-361. Zbl0314.57018
  8. [8] H. Winkelnkemper, The graph of a foliation, Ann. Global Anal. Geom. 1 (1983), 51-75. Zbl0526.53039
  9. [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. [10] R. A. Wolak, Foliations admitting transverse systems of differential equations, Compositio Math. 67 (1988), 89-101. Zbl0649.57027
  11. [11] R. A. Wolak, Le graphe d'un feuilletage admettant un système d'équations différentielles, Math. Z. 201 (1989), 177-182. Zbl0645.57022
  12. [12] R. A. Wolak, Geometric Structures on Foliated Manifolds, Universidad de Santiago de Compostela, 1989 Zbl0838.53029
  13. [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 

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