Displaying similar documents to “Certain curvature characterizations of affine hypersurfaces”

Hypersurfaces with parallel affine curvature tensor R*

Barbara Opozda, Leopold Verstraelen (1999)

Annales Polonici Mathematici

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In [OV] we introduced an affine curvature tensor R*. Using it we characterized some types of hypersurfaces in the affine space ℝ n + 1 . In this paper we study hypersurfaces for which R* is parallel relative to the induced connection.

On metrizability of locally homogeneous affine 2-dimensional manifolds

Alena Vanžurová (2013)

Archivum Mathematicum

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In [19] we proved a theorem which shows how to find, under particular assumptions guaranteeing metrizability (among others, recurrency of the curvature is necessary), all (at least local) pseudo-Riemannian metrics compatible with a given torsion-less linear connection without flat points on a two-dimensional affine manifold. The result has the form of an implication only; if there are flat points, or if curvature is not recurrent, we have no good answer in general, which can be also...