Geodesic
The Gauss-Bonnet Integrand for a Class of Riemannian Manifolds Admitting Two Orthogonal Complementary Foliations
Canadian mathematical bulletin, Tome 26 (1983) no. 3, pp. 358-364

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

With the general assumption that the manifold admits two orthogonal complementary foliations, one of which is totally geodesic, we study the components of the curvature tensor field of the characteristic connection.In the case where the manifold is compact, orientable of dimension 6 or 8 and the dimension of the totally geodesic foliation is 4, we relate the sign of the Euler characteristic of the manifold and that of the sectional curvature of the leaves of both foliations.
DOI : 10.4153/CMB-1983-061-8
Mots-clés : 53C15, 57R30, 57R20, Almost-product structure, characteristic connection, totally geodesic, totally umbilical, minimal foliation, Gauss-Bonnet integrand 
Gil-Medrano, O.; Naveira, A. M. The Gauss-Bonnet Integrand for a Class of Riemannian Manifolds Admitting Two Orthogonal Complementary Foliations. Canadian mathematical bulletin, Tome 26 (1983) no. 3, pp. 358-364. doi: 10.4153/CMB-1983-061-8
@article{10_4153_CMB_1983_061_8,
     author = {Gil-Medrano, O. and Naveira, A. M.},
     title = {The {Gauss-Bonnet} {Integrand} for a {Class} of {Riemannian} {Manifolds} {Admitting} {Two} {Orthogonal} {Complementary} {Foliations}},
     journal = {Canadian mathematical bulletin},
     pages = {358--364},
     year = {1983},
     volume = {26},
     number = {3},
     doi = {10.4153/CMB-1983-061-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-061-8/}
}
TY  - JOUR
AU  - Gil-Medrano, O.
AU  - Naveira, A. M.
TI  - The Gauss-Bonnet Integrand for a Class of Riemannian Manifolds Admitting Two Orthogonal Complementary Foliations
JO  - Canadian mathematical bulletin
PY  - 1983
SP  - 358
EP  - 364
VL  - 26
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-061-8/
DO  - 10.4153/CMB-1983-061-8
ID  - 10_4153_CMB_1983_061_8
ER  - 
%0 Journal Article
%A Gil-Medrano, O.
%A Naveira, A. M.
%T The Gauss-Bonnet Integrand for a Class of Riemannian Manifolds Admitting Two Orthogonal Complementary Foliations
%J Canadian mathematical bulletin
%D 1983
%P 358-364
%V 26
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-061-8/
%R 10.4153/CMB-1983-061-8
%F 10_4153_CMB_1983_061_8

[1] 1. Bishop, R. L. and Goldberg, S. I. Some implications of the generalized Gauss-Bonnet theorem. Trans. A.M.S. 112 (1964) 508–535. Google Scholar

[2] 2. Chern, S. S. On curvature and characteristic classes of a Riemannian manifold. Bull. A.M.S. 72 (1966) 167–219. Google Scholar

[3] 3. Gil-Medrano, , O. Geometric properties of some classes of Riemannian almost-product manifolds. Preprint. Google Scholar

[4] 4. V, Miquel. Some examples of Riemannian almost-product manifolds. Preprint. Google Scholar

[5] 5. Montesinos, A. On certain classes of almost-product structures. Preprint. Google Scholar

[6] 6. Naveira, A. M. A classification of Riemannian almost-product manifolds. Preprint. Google Scholar

Cité par Sources :