Geodesic
Totally geodesic submanifolds in the tangent bundle of a Riemannian 2-manifold
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 1 (2005) no. 1, pp. 116-139 Cet article a éte moissonné depuis la source Math-Net.Ru

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We give a full description of totally geodesic submanifolds in the tangent bundle of a Riemannian 2-manifold of constant curvature and present a new class of a cylinder-type totally geodesic submanifolds in the general case. 
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Alexander Yampolsky. Totally geodesic submanifolds in the tangent bundle of a Riemannian 2-manifold. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 1 (2005) no. 1, pp. 116-139. http://geodesic.mathdoc.fr/item/JMAG_2005_1_1_a6/

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