Geodesic
A Geometrical Theory of Multiple Integral Problems in the Calculus of Variations
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 639-657

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Let Xn denote an n-dimensional differentiate manifold referred to local coordinates x i . An m-dimensional subspace Cm (m < n) of Xn can be represented parametrically in the form 1.1 
Rund, H. A Geometrical Theory of Multiple Integral Problems in the Calculus of Variations. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 639-657. doi: 10.4153/CJM-1968-062-1
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