Torsion and the second fundamental form for distributions
journal contributionposted on 2022-05-11, 02:05 authored by Geoffrey PrinceGeoffrey Prince
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.