Geodesic
An Inverse Problem in the Calculus of Variations and the Characteristic Curves of Connections on SO(3)-Bundles
Canadian mathematical bulletin, Tome 38 (1995) no. 2, pp. 129-140

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This paper concerns an inverse problem in the calculus of variations, namely, when a two-dimensional symmetric connection is globally a Riemannian or pseudo-Riemannian connection. Two new local characterizations of such connections in terms of the Ricci tensor and the Riemann curvature tensor respectively are given, together with a solution to the global problem. As an application, the problem of whether the characteristic curves of a connection on an SO(3)-bundle on a surface are the geodesies of a Riemannian metric on the surface is studied. Some applications to non-holonomic dynamics are discussed.
DOI : 10.4153/CMB-1995-019-x
Mots-clés : 53C05, 53C22 
Atkins, Richard. An Inverse Problem in the Calculus of Variations and the Characteristic Curves of Connections on SO(3)-Bundles. Canadian mathematical bulletin, Tome 38 (1995) no. 2, pp. 129-140. doi: 10.4153/CMB-1995-019-x
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     title = {An {Inverse} {Problem} in the {Calculus} of {Variations} and the {Characteristic} {Curves} of {Connections} on {SO(3)-Bundles}},
     journal = {Canadian mathematical bulletin},
     pages = {129--140},
     year = {1995},
     volume = {38},
     number = {2},
     doi = {10.4153/CMB-1995-019-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1995-019-x/}
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