×

zbMATH — the first resource for mathematics

Geodesic shift in the space of supporting covector densities. (Russian) Zbl 0841.53022
In the paper there is considered the space \(X\) of supporting covector densities of weight \(-p\), i.e. the space of differential-geometric objects \(u_i\) with transformation rule \(u_{i'} = \Delta^p f^i_{i'} u_i\), where \(f^i_{i'} = {\partial x^i\over \partial x^{i'}}\), \(\Delta = \text{det }|f^i_{i'}|\), and \(u^i\) is equivalent to \(\lambda u^i\) (for the general theory see B. L. Laptev [Trudy Semin. Vektor. Tensor. Anal. 10, 227-248 (1956; Zbl 0074.16603)]. The author supplies \(X\) with a connection and finds conditions for a vector field \(V\) on \(X\) to be an infinitesimal transformation which sends affine paths into affine paths.
MSC:
53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)
53A55 Differential invariants (local theory), geometric objects
Citations:
Zbl 0074.16603
PDF BibTeX XML Cite
Full Text: EuDML