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1996 | 64 | 3 | 253-265
Tytuł artykułu

On the first secondary invariant of Molino's central sheaf

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For a Riemannian foliation on a closed manifold, the first secondary invariant of Molino's central sheaf is an obstruction to tautness. Another obstruction is the class defined by the basic component of the mean curvature with respect to some metric. Both obstructions are proved to be the same up to a constant, and other geometric properties are also proved to be equivalent to tautness.
Słowa kluczowe
EN
foliation   taut  
Rocznik
Tom
64
Numer
3
Strony
253-265
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-08-21
poprawiono
1995-11-29
Twórcy
  • Universidade de Santiago de Compostela, Facultade de Ciencias, 27071 Lugo, Spain
Bibliografia
  • [1] J. A. Álvarez López, A finiteness theorem for the spectral sequence of a Riemannian foliation, Illinois J. Math. 33 (1989), 79-92.
  • [2] J. A. Álvarez López, The basic component of the mean curvature of Riemannian foliations, Ann. Global Anal. Geom. 10 (1992), 179-194.
  • [3] J. A. Álvarez López, Morse inequalities for pseudogroups of local isometries, J. Differential Geom. 37 (1993), 603-638.
  • [4] Y. Carrière, Flots riemanniens, Astérisque 116 (1984), 31-52.
  • [5] D. Domínguez, Finiteness and tenseness theorems for Riemannian foliations, preprint, 1994.
  • [6] A. El Kacimi-Alaoui et G. Hector, Décomposition de Hodge sur l'espace des feuilles d'un feuilletage riemannien, C. R. Acad. Sci. Paris 298 (1984), 289-292.
  • [7] A. El Kacimi-Alaoui, G. Hector et V. Sergiescu, La cohomologie basique d'un feuilletage Riemannien est de dimension finie, Math. Z. 188 (1985), 593-599.
  • [8] A. El Kacimi-Alaoui and M. Nicolau, On the topological invariance of the basic cohomology, Math. Ann. 293 (1993), 627-634.
  • [9] A. Haefliger, Some remarks on foliations with minimal leaves, J. Differential Geom. 15 (1980), 269-384.
  • [10] A. Haefliger, Pseudogroups of local isometries, in: Differential Geometry, Proc. Conf. Santiago de Compostela 1984, L. A. Cordero (ed.), Pitman, 1984, 174-197.
  • [11] A. Haefliger, Leaf Closures in Riemannian Foliations, in: A Fête on Topology, Academic Press, New York, 1988, 3-32.
  • [12] F. Kamber and P. Tondeur, Foliated Bundles and Characteristic Classes, Lecture Notes in Math. 494, Springer, 1975.
  • [13] F. Kamber and P. Tondeur, De Rham-Hodge theory for Riemannian foliations, Math. Ann. 277 (1987), 415-431.
  • [14] E. Macías and E. Sanmartín, Minimal foliations on Lie groups, Indag. Math. 3 (1992), 41-46.
  • [15] X. Masa, Duality and minimality in Riemannian foliations, Comment. Math. Helv. 67 (1992), 17-27.
  • [16] P. Molino, Géométrie globale des feuilletages riemanniens, Nederl. Akad. Wetensch. Proc. A1 85 (1982), 45-76.
  • [17] P. Molino, Riemannian Foliations, Progr. Math. 73, Birkhäuser, Boston, 1988.
  • [18] P. Molino et V. Sergiescu, Deux remarques sur les flots riemanniens, Manuscripta Math. 51 (1985), 145-161.
  • [19] B. L. Reinhart, Foliated manifolds with bundle-like metrics, Ann. of Math. 69 (1959), 119-132.
  • [20] H. Rummler, Quelques notions simples en géométrie riemannienne et leurs applications aux feuilletages compacts, Comment. Math. Helv. 54 (1979), 224-239.
  • [21] E. Salem, Riemannian foliations and pseudogroups of isometries, in: Riemannian Foliations, Progr. Math. 73, Birkhäuser, Boston, 1988.
  • [22] V. Sergiescu, Cohomologie basique et dualité des feuilletages riemanniens, Ann. Inst. Fourier (Grenoble) 35 (1985), 137-158.
  • [23] A. Verona, A de Rham type theorem, Proc. Amer. Math. Soc. 104 (1988), 300-302.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv64z3p253bwm
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