Indefinite affine hyperspheres admitting a pointwise symmetry. II.
Scharlach, Christine (2009)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Scharlach, Christine (2009)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Felaco, Elisabetta, Giuli, Eraldo (2008)
Theory and Applications of Categories [electronic only]
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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...
Lam, Thomas, Shimozono, Mark (2005)
Séminaire Lotharingien de Combinatoire [electronic only]
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Scharlach, Christine (2007)
Beiträge zur Algebra und Geometrie
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Tyszka, Apoloniusz (2005)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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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.
Ito, Tatsuro, Terwilliger, Paul (2010)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Ljubiša Kocić, Marija Rafajlović (2010)
Kragujevac Journal of Mathematics
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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.
Chen, Bang-Yen (2006)
Beiträge zur Algebra und Geometrie
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Azam, Saeid (2002)
Journal of Lie Theory
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Karol Pąk (2011)
Formalized Mathematics
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In this paper we present selected properties of barycentric coordinates in the Euclidean topological space. We prove the topological correspondence between a subset of an affine closed space of εn and the set of vectors created from barycentric coordinates of points of this subset.