Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Invariants and Bonnet-type theorem for surfaces in ℝ4

100%

Ganchev G., Milousheva V.

Open Mathematics

2010

tom 8

nr 6

993-1008

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.

Ograniczanie wyników

1 Open Mathematics

1 Ganchev G.

1 Milousheva V.

1 2010

Wyniki wyszukiwania

Invariants and Bonnet-type theorem for surfaces in ℝ4