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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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  • [3] Chen B.-Y., Geometry of Submanifolds, Pure and Applied Mathematics, 22, Marcel Dekker, New York, 1973
  • [4] Chen B.-Y., Classification of Wintgen ideal surfaces in Euclidean 4-space with equal Gauss and normal curvatures, Ann. Global Anal. Geom., 2010, 38(2), 145–160 http://dx.doi.org/10.1007/s10455-010-9205-5
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  • [13] Guadalupe I.V., Rodriguez L., Normal curvature of surfaces in space forms, Pacific J. Math., 1983, 106(1), 95–103
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  • [17] Petrović-Torgašev M., Verstraelen L., On Deszcz symmetries of Wintgen ideal submanifolds, Arch. Math. (Brno), 2008, 44(1), 57–67
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Bibliografia

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bwmeta1.element.doi-10_2478_s11533-010-0073-9
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