| Title:
|
Torsion and the second fundamental form for distributions (English) |
| Author:
|
Prince, Geoff |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 |
| Volume:
|
24 |
| Issue:
|
1 |
| Year:
|
2016 |
| Pages:
|
23-28 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The second fundamental form of Riemannian geometry is generalised to the case of a manifold with a linear connection and an integrable distribution. This bilinear form is generally not symmetric and its skew part is the torsion. The form itself is closely related to the shape map of the connection. The codimension one case generalises the traditional shape operator of Riemannian geometry. (English) |
| Keyword:
|
Torsion |
| Keyword:
|
second fundamental form |
| Keyword:
|
shape operator |
| Keyword:
|
integrable distributions |
| MSC:
|
53B05 |
| MSC:
|
53C05 |
| MSC:
|
58A10 |
| idZBL:
|
Zbl 1354.53027 |
| idMR:
|
MR3546804 |
| . |
| Date available:
|
2016-08-26T11:17:14Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145803 |
| . |
| Reference:
|
[1] Bejancu, A., Farran, H.R.: Foliations and Geometric Structures.2006, Springer, Zbl 1092.53021, MR 2190039 |
| Reference:
|
[2] Crampin, M., Prince, G.E.: The geodesic spray, the vertical projection, and Raychaudhuri's equation..Gen. Rel. Grav., 16, 1984, 675-689, Zbl 0541.53012, MR 0750379, 10.1007/BF00767860 |
| Reference:
|
[3] Jerie, M., Prince, G.E.: A generalised Raychaudhuri equation for second–order differential equations.J. Geom. Phys., 34, 3, 2000, 226-241, MR 1762775, 10.1016/S0393-0440(99)00065-0 |
| Reference:
|
[4] Jerie, M., Prince, G.E.: Jacobi fields and linear connections for arbitrary second order ODE's..J. Geom. Phys., 43, 4, 2002, 351-370, MR 1929913, 10.1016/S0393-0440(02)00030-X |
| Reference:
|
[5] Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry.1, 1963, Wiley-Interscience, New York, Zbl 0119.37502, MR 0152974 |
| Reference:
|
[6] Lee, J. M.: Riemannian manifolds: an introduction to curvature.1997, Springer-Verlag, New York, Zbl 0905.53001, MR 1468735 |
| . |
