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2010 | 8 | 6 | 993-1008
Tytuł artykułu

Invariants and Bonnet-type theorem for surfaces in ℝ4

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the tangent plane at any point of a surface in the four-dimensional Euclidean space we consider an invariant linear map ofWeingarten-type and find a geometrically determined moving frame field. Writing derivative formulas of Frenet-type for this frame field, we obtain eight invariant functions. We prove a fundamental theorem of Bonnet-type, stating that these eight invariants under some natural conditions determine the surface up to a motion. We show that the basic geometric classes of surfaces in the four-dimensional Euclidean space, determined by conditions on their invariants, can be interpreted in terms of the properties of two geometric figures: the tangent indicatrix, which is a conic in the tangent plane, and the normal curvature ellipse. We construct a family of surfaces with flat normal connection.
Wydawca
Czasopismo
Rocznik
Tom
8
Numer
6
Strony
993-1008
Opis fizyczny
Daty
wydano
2010-12-01
online
2010-10-30
Twórcy
Bibliografia
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-010-0073-9
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