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On the Pontrjagin Algebra of a Certain Class of Flags of Foliations

  • F. J. Carreras (a1) and A. M. Naveira (a1)

Abstract

Let (𝓜,g) be a Riemannian manifold and let 1, 2, 3 be mutually orthogonal distributions on 𝓜 of dimensions p1, p2,P3 such that p1 + p2 + p3 = dim 𝓜. We assume that , and 1, ⊕ 2 are integrable and that all the geodesies of 𝓜 with initial tangent vector in 2 remain tangent to 2. Then, we prove that Pontk( 2, ⊕ 3) = 0 for k > p2 + 2p3, where Pontk( 2, ⊕ 3) is the subspace of the Pontrjagin algebra of 2 3 generated by forms of degree k.

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References

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1. Bott, R., Lectures on characteristic classes and foliations, Lecture Notes in Mathematics, Springer-Verlag, 279(1972), pp. 180.
2. Cordero, L.A. and Masa, X., Characteristic classes of subfoliations, Ann. Inst. Fourier, Grenoble 31, 2 (1981), pp. 6186.
3. Gil-Medrano, O., On the geometric properties of some classes of almost-product structures, Rend. Circ. Mat. Palermo 32 (1983), 315-329.
4. Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry, Vol. I and II, Interscience, 1963, 1969.
5. Miquel, V., Some examples of Riemannian almost-product manifolds, Pac. J. Math. III (1984), 163178.
6. Naveira, A.M., A classification of Riemannian almost-product manifolds, Rendiconti di Matematica, 3 (1983), 577-592.
7. Pasternack, J.S., Foliations and compact Lie group actions, Comm. Math. Helv. 46 (1971), pp. 467477.
8. Reinhart, B., Foliated manifolds with bundle-like metrics, Ann. of Math. 69 (1959), pp. 119131.
9. Vaisman, I., Almost-multifoliate Riemannian manifolds, Ann. St. Univ. “Al. I. Cuza”, XVI (1970), pp. 97104.
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