A metric formula for the Godbillon-Vay invariant for foliations
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- by Bruce L. Reinhart and John W. Wood PDF
- Proc. Amer. Math. Soc. 38 (1973), 427-430 Request permission
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
- Claude Godbillon and Jacques Vey, Un invariant des feuilletages de codimension $1$, C. R. Acad. Sci. Paris Sér. A-B 273 (1971), A92-A95 (French). MR 283816
- D. Gromoll, W. Klingenberg, and W. Meyer, Riemannsche Geometrie im Grossen, Lecture Notes in Mathematics, No. 55, Springer-Verlag, Berlin-New York, 1968 (German). MR 0229177, DOI 10.1007/978-3-540-35901-2
- Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol I, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1963. MR 0152974
Additional Information
- © Copyright 1973 American Mathematical Society
- 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