Displaying similar documents to “Eigenvalues of a natural operator of centro-affine and graph 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.

Affine surfaces with parallel shape operators

Włodzimierz Jelonek (1992)

Annales Polonici Mathematici

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We study affine nondegenerate Blaschke hypersurfaces whose shape operators are parallel with respect to the induced Blaschke connections. We classify such surfaces and thus give an exact classification of extremal locally symmetric surfaces, first described by F. Dillen.

Affine Independence in Vector Spaces

Karol Pąk (2010)

Formalized Mathematics

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In this article we describe the notion of affinely independent subset of a real linear space. First we prove selected theorems concerning operations on linear combinations. Then we introduce affine independence and prove the equivalence of various definitions of this notion. We also introduce the notion of the affine hull, i.e. a subset generated by a set of vectors which is an intersection of all affine sets including the given set. Finally, we introduce and prove selected properties...

Abstract separation theorems of Rodé type and their applications

Kazimierz Nikodem, Zsolt Páles, Szymon Wąsowicz (1999)

Annales Polonici Mathematici

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Sufficient and necessary conditions are presented under which two given functions can be separated by a function Π-affine in Rodé sense (resp. Π-convex, Π-concave). As special cases several old and new separation theorems are obtained.