Displaying similar documents to “On the energy of unit vector fields with isolated singularities”

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...

De Lellis-Topping type inequalities for f-Laplacians

Guangyue Huang, Fanqi Zeng (2016)

Studia Mathematica

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We establish an integral geometric inequality on a closed Riemannian manifold with ∞-Bakry-Émery Ricci curvature bounded from below. We also obtain similar inequalities for Riemannian manifolds with totally geodesic boundary. In particular, our results generalize those of Wu (2014) for the ∞-Bakry-Émery Ricci curvature.