Tangent curves are a powerful tool for analysing and visualizing vector fields. For sufficiently complicated vector fields they can only be implicitly described. However, in this work two of their most important properties will be studied: their curvature and torsion. Both of them can be computed only by knowing the partial derivates of a vector field. Furthermore, the new concept of normal surfaces and their Gaussian and mean curvature will be introduced to the theory of vector fields. For curvature, torsion, Gaussian and mean curvature it can be shown that at least one of the scalar fields describing these measures tends to infinity in the neighborhood around a critical point of a linear vector field. Therefore, the visualization of those scalar fields has a topological relevance. Several visualization techniques for this purpose will be discussed. Furthermore, it can be shown that the mean curvature uniquely describes linear vector fields in canonical form.


List of all publications