Geodesic
Torsion and the second fundamental form for distributions
Communications in Mathematics, Tome 24 (2016) no. 1, pp. 23-28
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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.
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.
Classification : 53B05, 53C05, 58A10
Keywords: Torsion; second fundamental form; shape operator; integrable distributions 
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Prince, Geoff. Torsion and the second fundamental form for distributions. Communications in Mathematics, Tome 24 (2016) no. 1, pp. 23-28. http://geodesic.mathdoc.fr/item/COMIM_2016_24_1_a2/

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