Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geodesic Orbit Riemannian Structures on $\mathbf{R}^n$   A geodesic orbit manifold is a complete Riemannian manifold all of whose
geodesics are orbits of one-parameter groups of isometries. We give both a
geometric and an algebraic characterization of geodesic orbit manifolds that
are diffeomorphic to $\mathbf{R}^n$. Along the way, we establish various
structural properties of more general geodesic orbit manifolds.

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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: eess