Geometric interpretation of the invariants of a surface in R^4 via the tangent indicatrix and the normal curvature ellipse

Details Geometric interpretation of the invariants of a surface in R^4 via the tangent indicatrix and the normal curvature ellipse Geometric interpretation of the invariants of a surface in R^4 via the tangent indicatrix and the normal curvature ellipse

2009-05-27

arxiv.org/abs/0905.4453v1

Mathematics

Differential Geometry

13 pages

Scientific paper

At any point of a surface in the four-dimensional Euclidean space we consider the geometric configuration consisting of two figures: the tangent indicatrix, which is a conic in the tangent plane, and the normal curvature ellipse. 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 the two geometric figures. We give some non-trivial examples of surfaces from the classes in consideration.

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