CONTENTSI. 1. Introduction..................................................................................................................................................................5 2. Preliminaries..............................................................................................................................................................11 3. On Simon’s conjecture..............................................................................................................................................13II....
CONTENTSIntroduction.................................................................................................................................................51. Preliminaries...........................................................................................................................................62. f-Kählerian manifolds............................................................................................................................113. The f-sectional curvature...
In [OV] we introduced an affine curvature tensor R*. Using it we characterized some types of hypersurfaces in the affine space . In this paper we study hypersurfaces for which R* is parallel relative to the induced connection.
We investigate parallel hypersurfaces in the context of relative hypersurface geometry, in particular including the cases of Euclidean and Blaschke hypersurfaces. We describe the geometric relations between parallel hypersurfaces in terms of deformation operators, and we apply the results to the parallel deformation of special classes of hypersurfaces, e.g. quadrics and Weingarten hypersurfaces.
The aim of this paper is to classify (lócally) all torsion-less locally homogeneous affine connections on two-dimensional manifolds from a group-theoretical point of view. For this purpose, we are using the classification of all non-equivalent transitive Lie algebras of vector fields in ℝ2 according to P.J. Olver [7].
Curvature homogeneity of (torsion-free) affine connections on manifolds is an adaptation of a concept introduced by I. M. Singer. We analyze completely the relationship between curvature homogeneity of higher order and local homogeneity on two-dimensional manifolds.
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