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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
##### Keywords:
covector density; affine path; Lie derivative
Zbl 0074.16603
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