We consider the variational problem for curves in real projective plane defined by the projective arclength functional and discuss the integrability of its stationary curves in a geometric setting. We show how methods from the subject of exterior differential systems and the reduction procedure for Hamiltonian systems with symmetries lead to the integration by quadratures of the extrema. A scheme of integration is illustrated.
Reduction for the projective arclength functional / Musso, E; Nicolodi, Lorenzo. - In: FORUM MATHEMATICUM. - ISSN 0933-7741. - 17:4(2005), pp. 569-590. [10.1515/form.2005.17.4.569]
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