Displaying similar documents to “Indefinite affine hyperspheres admitting a pointwise symmetry. II.”

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...

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.

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.

Mazur-Ulam Theorem

Artur Korniłowicz (2011)

Formalized Mathematics

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The Mazur-Ulam theorem [15] has been formulated as two registrations: cluster bijective isometric -> midpoints-preserving Function of E, F; and cluster isometric midpoints-preserving -> Affine Function of E, F; A proof given by Jussi Väisälä [23] has been formalized.

Geometry of control-affine systems.

Clelland, Jeanne N., Moseley, Christopher G., Wilkens, George R. (2009)

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

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