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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.

Torsions of connections on higher order cotangent bundles

Miroslav Doupovec, Jan Kurek (2003)

Czechoslovak Mathematical Journal

By a torsion of a general connection Γ on a fibered manifold Y M we understand the Frölicher-Nijenhuis bracket of Γ and some canonical tangent valued one-form (affinor) on Y . Using all natural affinors on higher order cotangent bundles, we determine all torsions of general connections on such bundles. We present the geometrical interpretation and study some properties of the torsions.

Torsions of connections on time-dependent Weil bundles

Miroslav Doupovec (2003)

Colloquium Mathematicae

We introduce the concept of a dynamical connection on a time-dependent Weil bundle and we characterize the structure of dynamical connections. Then we describe all torsions of dynamical connections.

Total connections in Lie groupoids

Juraj Virsik (1995)

Archivum Mathematicum

A total connection of order r in a Lie groupoid Φ over M is defined as a first order connections in the ( r - 1 ) -st jet prolongations of Φ . A connection in the groupoid Φ together with a linear connection on its base, ie. in the groupoid Π ( M ) , give rise to a total connection of order r , which is called simple. It is shown that this simple connection is curvature-free iff the generating connections are. Also, an r -th order total connection in Φ defines a total reduction of the r -th prolongation of Φ to Φ × Π ( M ) ....

Two-spinor tetrad and Lie derivatives of Einstein-Cartan-Dirac fields

Daniel Canarutto (2018)

Archivum Mathematicum

An integrated approach to Lie derivatives of spinors, spinor connections and the gravitational field is presented, in the context of a previously proposed, partly original formulation of a theory of Einstein-Cartan-Maxwell-Dirac fields based on “minimal geometric data”: the needed underlying structure is determined, via geometric constructions, from the unique assumption of a complex vector bundle S M with 2-dimensional fibers, called a 2 -spinor bundle. Any further considered object is assumed to...

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