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Higher order connections.

Eastwood, Michael G. (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Homogeneous Geodesics in 3-dimensional Homogeneous Affine Manifolds

Zdeněk Dušek, Oldřich Kowalski, Zdeněk Vlášek (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

For studying homogeneous geodesics in Riemannian and pseudo-Riemannian geometry (on reductive homogeneous spaces) there is a simple algebraic formula which works, at least potentially, in every given case. In the affine differential geometry, there is not such a universal formula. In the previous work, we proposed a simple method of investigation of homogeneous geodesics in homogeneous affine manifolds in dimension 2. In the present paper, we use this method on certain classes of homogeneous connections...

Horizontal lift of symmetric connections to the bundle of volume forms ν

Anna Gąsior (2010)

Annales UMCS, Mathematica

In this paper we present the horizontal lift of a symmetric affine connection with respect to another affine connection to the bundle of volume forms ν and give formulas for its curvature tensor, Ricci tensor and the scalar curvature. Next, we give some properties of the horizontally lifted vector fields and certain infinitesimal transformations. At the end, we consider some substructures of a F(3, 1)-structure on ν.

How many are affine connections with torsion

Zdeněk Dušek, Oldřich Kowalski (2014)

Archivum Mathematicum

The question how many real analytic affine connections exist locally on a smooth manifold M of dimension n is studied. The families of general affine connections with torsion and with skew-symmetric Ricci tensor, or symmetric Ricci tensor, respectively, are described in terms of the number of arbitrary functions of n variables.

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