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Proceedings of the American Mathematical Society

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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
DOI: https://doi.org/10.1090/S0002-9939-1973-0310907-5
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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0310907-5
Keywords: Godbillon-Vey invariant, Frenet formulas, second fundamental form
Article copyright: © Copyright 1973 American Mathematical Society