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A metric formula for the Godbillon-Vay invariant for foliations

Authors: Bruce L. Reinhart and John W. Wood
Journal: Proc. Amer. Math. Soc. 38 (1973), 427-430
MSC: Primary 57D30; Secondary 53C40
MathSciNet review: 0310907
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Abstract: The Godbillon-Vey invariant for a foliation of codimension 1 is acohomology class defined by a $ 3$-form. On a Riemannian manifold, this form can be expressed in terms of the curvature and torsion of the normal curve family and the second fundamental form of the leaves.

References [Enhancements On Off] (What's this?)

  • [1] C. Godbillon and J. Vey, Un invariant des feuilletages de codimension 1, C. R. Acad. Sci. Paris Sér. A-B 273 (1971), A92-A95. MR 44 #1046. MR 0283816 (44:1046)
  • [2] D. Gromoll, W. Klingenberg and W. Meyer, Riemannsche Geometrie im Grossen, Lecture Notes in Math., no. 55, Springer-Verlag, Berlin and New York, 1968. MR 37 #4751. MR 0229177 (37:4751)
  • [3] S. Kobayashi and K. Nomizu, Foundations of differential geometry. Vol. I, Inter-science, New York, 1963. MR 27 #2945. MR 0152974 (27:2945)

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Keywords: Godbillon-Vey invariant, Frenet formulas, second fundamental form
Article copyright: © Copyright 1973 American Mathematical Society

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