``Meta''-rigid motions and frames of reference
The authors define meta-rigid motions as particular classes of time-like congruences which are solutions of intrinsically defined partial differential equations that generalize Born's conditions. As the authors say, most of the concepts introduced here in the geometry of time-like congruences such as transverse partial derivative, the connection symbols that the authors call Cattaneo quo-connection, and the Cattaneo quo-tensor, have been borrowed from Cattaneo's papers (see for instance \textit{C. Cattaneo} [Ann. Mat. Pura Appl., IV. Ser. 48, 361-386 (1959; Zbl 0090.18803)]). In general the authors call quo-tensors the geometric objects defined on the quotient manifold which transform as scalars under time-gauge transformations and as tensors under pure space transformations. Born congruences have the property that the spacetime metric can be projected on the quotient manifold, giving a metric independent of time, and thus are called by the authors quo-isometries. The first generalization is to consider quo-similarities: They are congruences for which the Cattaneo connection is independent of time and thus induces on the quotient manifold a linear connection which is in general not Euclidean. The second generalization is to consider quo-collineations as the congruences for which the four index Cattaneo quo-tensor is time-independent. All these congruences are defined by differential equations for which data on the world line define unique solutions, when they exist. A more indirect generalization is based on the conditions which guarantee the existence of a particular class of adapted quo-harmonic coordinates, namely harmonic with respect to a generalized Laplacian defined on the quotient manifold.
scientific article; zbMATH DE number 826719