Displaying similar documents to “On the geometry of Riemannian manifolds with a Lie structure at infinity.”

Connection induced geometrical concepts

Musilová, Pavla, Musilová, Jana

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Summary: Geometrical concepts induced by a smooth mapping f : M N of manifolds with linear connections are introduced, especially the (higher order) covariant differentials of the mapping tangent to f and the curvature of a corresponding tensor product connection. As an useful and physically meaningful consequence a basis of differential invariants for natural operators of such smooth mappings is obtained for metric connections. A relation to geometry of Riemannian manifolds is discussed. ...

Lorentzian manifolds with special holonomy and parallel spinors

Leistner, Thomas

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The author studies the holonomy group of a simply connected indecomposable and reducible Lorentzian spin manifold under the condition that they admit parallel spinors. He shows that there are only two possible situations: either the manifold is a so-called Brinkmann wave or it has Abelian holonomy and is a pp-manifold – a generalization of a plane-wave. The author gives also sufficient conditions for a Brinkmann wave to have as holonomy the semidirect product of holonomy group of a Riemannian...