Geodesic
Note on Almost Product Manifolds and their Tangent Bundles
Canadian mathematical bulletin, Tome 9 (1966) no. 5, pp. 621-630

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

Let Mn be an n-dimensional manifold of differentiability class C∞ with an almost product structure . Let have eigenvalue +1 of multiplicity p and eigenvalue -1 of multiplicity q where p+q = n and p≧1, q≧1. Let T(Mn) be the tangent bundle of M. T(Mn) is a 2n dimensional manifold of class C∞. Let xi be the local coordinates of a point P of Mn. The local coordinates of T(Mn) can be expressed by 2n variables (xi, yi) where xi are coordinates of the point P and yi are components of a tangent vector at P with respect to the natural frame constituted by the vectior ∂/∂xi at P. 
Houh, Chorng Shi. Note on Almost Product Manifolds and their Tangent Bundles. Canadian mathematical bulletin, Tome 9 (1966) no. 5, pp. 621-630. doi: 10.4153/CMB-1966-075-0
@article{10_4153_CMB_1966_075_0,
     author = {Houh, Chorng Shi},
     title = {Note on {Almost} {Product} {Manifolds} and their {Tangent} {Bundles}},
     journal = {Canadian mathematical bulletin},
     pages = {621--630},
     year = {1966},
     volume = {9},
     number = {5},
     doi = {10.4153/CMB-1966-075-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1966-075-0/}
}
TY  - JOUR
AU  - Houh, Chorng Shi
TI  - Note on Almost Product Manifolds and their Tangent Bundles
JO  - Canadian mathematical bulletin
PY  - 1966
SP  - 621
EP  - 630
VL  - 9
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1966-075-0/
DO  - 10.4153/CMB-1966-075-0
ID  - 10_4153_CMB_1966_075_0
ER  - 
%0 Journal Article
%A Houh, Chorng Shi
%T Note on Almost Product Manifolds and their Tangent Bundles
%J Canadian mathematical bulletin
%D 1966
%P 621-630
%V 9
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1966-075-0/
%R 10.4153/CMB-1966-075-0
%F 10_4153_CMB_1966_075_0

[1] 1. Hsu, C.J., On some structures which are similar to the quaternion structure. TɄhoku Math. J. 12, (1960), pages 403-428. Google Scholar

[2] 2. Hsu, C. J., Remarks on certain almost product spaces. Pacific J. Math., 14, (1964), pages 163-176. Google Scholar

[3] 3. Sasaki, S., On the differential geometry of tangent bundles of Riemannian manifolds. TɄhoku Math. J. 10, (1958), pages 338-354. Google Scholar

[4] 4. Tachibana, S. and Okumura, M., On the almost-complex structure of tangent bundles of Riemannian spaces. T?hoku Math. J. 14, (1962), pages 156-161. Google Scholar

[5] 5. Yano, K., Affine connections in an almost product space. Kadai Math. Sem. Rep. 11, (1959), pages 1-24. Google Scholar

[6] 6. Yano, K., Differential geometry on complex and almost complex spaces. Pergamon Press, (1965). Google Scholar

Cité par Sources :