The Topology of Three-Dimensional Symmetric Tensor Fields

We study the topology of 3-D symmetric tensor elds. The goal is to represent their complex structure by a simple set of carefully chosen points and lines analogous to vector eld topology. The basic constituents of tensor topology are the degenerate points, or points where eigenvalues are equal to each other. First, we introduce a new method for locating 3-D degenerate points. We then extract the topological skeletons of the eigenvector elds and use them for a compact, comprehensive description of the tensor eld. Finally, we demonstrate the use of tensor eld topology for the interpretation of the two-force Boussinesq problem.