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Torsion and the second fundamental form for distributions

Geoff Prince (2016)

Communications in Mathematics

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.

Vector form brackets in Lie algebroids

Albert Nijenhuis (1996)

Archivum Mathematicum

A brief exposition of Lie algebroids, followed by a discussion of vector forms and their brackets in this context - and a formula for these brackets in “deformed” Lie algebroids.

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