Abstract:
The subject of the paper are $G$-structures that are locally transitive with respect to dif-feomorphisms $f$ such that $\omega f^*=l\omega$, where $\omega$ is the displacement form, $l$ is an element of the centralizer of the structure group. In the involutive case we establish a necessary and sufficient condition for an arbitrary $G$-structure to be $Z$-transitive. As an example, we deduce the homo¬geneity criterion for Riemannian manifolds originally found by I. Singer. A description in terms of Lie groups is provided for arbitrary $Z$-transitive structures with finite-dimensional automorphism group.
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