Basic forms for transversely integrable singular Riemannian foliations

Wolak, Robert

doi:10.1090/S0002-9939-99-05316-2

Basic forms for transversely integrable singular Riemannian foliations
HTML articles powered by AMS MathViewer

by Robert A. Wolak PDF

Proc. Amer. Math. Soc. 128 (2000), 1543-1545 Request permission

Abstract:

Basic forms for a transversely integrable singular Riemannian foliation with compact leaves are in one-to-one correspondence with “Weyl"–invariant differential forms on a generalized section of the foliation.

References

R. A. Blumenthal and J. J. Hebda, de Rham decomposition theorems for foliated manifolds, Ann. Inst. Fourier (Grenoble) 33 (1983), no. 2, 183–198. MR 699494, DOI 10.5802/aif.923
H. Boualem, Feuilletages riemanniens singuliers transversalement intégrables, Compositio Math. 95 (1995), no. 1, 101–125 (French). MR 1314698
Peter W. Michor, Basic differential forms for actions of Lie groups, Proc. Amer. Math. Soc. 124 (1996), no. 5, 1633–1642. MR 1307550, DOI 10.1090/S0002-9939-96-03195-4
Peter W. Michor, Basic differential forms for actions of Lie groups. II, Proc. Amer. Math. Soc. 125 (1997), no. 7, 2175–2177. MR 1401750, DOI 10.1090/S0002-9939-97-03929-4
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
Richard S. Palais and Chuu-Lian Terng, Critical point theory and submanifold geometry, Lecture Notes in Mathematics, vol. 1353, Springer-Verlag, Berlin, 1988. MR 972503, DOI 10.1007/BFb0087442