Geodesic
On the Pontrjagin Algebra of a Certain Class of Flags of Foliations
Canadian mathematical bulletin, Tome 28 (1985) no. 1, pp. 77-83

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-1985-007-8
Mots-clés : 53C15, flag manifolds, bundle-like metrics, Pontrjagin algebra of a vector bundle 
Carreras, F. J.; Naveira, A. M. On the Pontrjagin Algebra of a Certain Class of Flags of Foliations. Canadian mathematical bulletin, Tome 28 (1985) no. 1, pp. 77-83. doi: 10.4153/CMB-1985-007-8
@article{10_4153_CMB_1985_007_8,
     author = {Carreras, F. J. and Naveira, A. M.},
     title = {On the {Pontrjagin} {Algebra} of a {Certain} {Class} of {Flags} of {Foliations}},
     journal = {Canadian mathematical bulletin},
     pages = {77--83},
     year = {1985},
     volume = {28},
     number = {1},
     doi = {10.4153/CMB-1985-007-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1985-007-8/}
}
TY  - JOUR
AU  - Carreras, F. J.
AU  - Naveira, A. M.
TI  - On the Pontrjagin Algebra of a Certain Class of Flags of Foliations
JO  - Canadian mathematical bulletin
PY  - 1985
SP  - 77
EP  - 83
VL  - 28
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1985-007-8/
DO  - 10.4153/CMB-1985-007-8
ID  - 10_4153_CMB_1985_007_8
ER  - 
%0 Journal Article
%A Carreras, F. J.
%A Naveira, A. M.
%T On the Pontrjagin Algebra of a Certain Class of Flags of Foliations
%J Canadian mathematical bulletin
%D 1985
%P 77-83
%V 28
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1985-007-8/
%R 10.4153/CMB-1985-007-8
%F 10_4153_CMB_1985_007_8

[1] 1. Bott, R., Lectures on characteristic classes and foliations, Lecture Notes in Mathematics, Springer-Verlag, 279(1972), pp. 1–80. Google Scholar

[2] 2. Cordero, L.A. and Masa, X., Characteristic classes of subfoliations, Ann. Inst. Fourier, Grenoble 31, 2 (1981), pp. 61–86. Google Scholar

[3] 3. Gil-Medrano, O., On the geometric properties of some classes of almost-product structures, Rend. Circ. Mat. Palermo 32 (1983), 315-329. Google Scholar

[4] 4. Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry, Vol. I and II, Interscience, 1963, 1969. Google Scholar

[5] 5. Miquel, V., Some examples of Riemannian almost-product manifolds, Pac. J. Math. III (1984), 163–178. Google Scholar

[6] 6. Naveira, A.M., A classification of Riemannian almost-product manifolds, Rendiconti di Matematica, 3 (1983), 577-592. Google Scholar

[7] 7. Pasternack, J.S., Foliations and compact Lie group actions, Comm. Math. Helv. 46 (1971), pp. 467–477. Google Scholar

[8] 8. Reinhart, B., Foliated manifolds with bundle-like metrics, Ann. of Math. 69 (1959), pp. 119–131. Google Scholar

[9] 9. Vaisman, I., Almost-multifoliate Riemannian manifolds, Ann. St. Univ. “Al. I. Cuza”, XVI (1970), pp. 97–104. Google Scholar

Cité par Sources :