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Displaying similar documents to “Killing graphs with prescribed mean curvature and riemannian submersions”

On the intrinsic geometry of a unit vector field

Yampolsky, Alexander L. Yampolsky, Alexander L. (2002)

Commentationes Mathematicae Universitatis Carolinae

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We study the geometrical properties of a unit vector field on a Riemannian 2-manifold, considering the field as a local imbedding of the manifold into its tangent sphere bundle with the Sasaki metric. For the case of constant curvature K , we give a description of the totally geodesic unit vector fields for K = 0 and K = 1 and prove a non-existence result for K 0 , 1 . We also found a family ξ ω of vector fields on the hyperbolic 2-plane L 2 of curvature - c 2 which generate foliations on T 1 L 2 with leaves of constant...