Remark on mixed foliate generic submanifolds
Totally real submanifolds of with parallel second fundamental form
Some contributions to the differential geometry of submanifolds
CONTENTSI. 1. Introduction..................................................................................................................................................................5 2. Preliminaries..............................................................................................................................................................11 3. On Simon’s conjecture..............................................................................................................................................13II....
Metric polynomial structures
CONTENTSIntroduction.................................................................................................................................................51. Preliminaries...........................................................................................................................................62. f-Kählerian manifolds............................................................................................................................113. The f-sectional curvature...
A class of projectively flat surfaces.
Some Equivalence Theorems in Affine Hypersurface Theory.
A Characterization of Affine Cylinders.
Generic submanifolds in almost Hermitian manifolds
The f-sectional curvature of f-Kaehlerian manifolds
On totally umbilical submanifolds in nearly Kählerian manifolds
Hypersurfaces with parallel affine curvature tensor R*
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.
Parallel hypersurfaces
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.
A classification of locally homogeneous connections on 2-dimensional manifolds via group-theoretical approach
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 affine connections on two-dimensional manifolds
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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