Characterization of 3D Sasakian manifold from magnetic Hopf surfaces

2019/11/30 by Satsuki Matsuno, Matsuno, Satsuki
Engineering · Mathematics · #3D Shape Modeling and Analysis #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1912.00165

openalex publication_date 2019/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a three-dimensional Riemannian manifold M that admits a unit Killing vector field ξ, we regard ξ as a magnetic vector field. A magnetic Hopf surface is a surface obtained by Lie dragging the magnetic curve with ξ. Then we characterize Sasakian structure on M from magnetic Hopf surfaces. That is, we show that if an arbitrary magnetic Hopf surface is a constant mean curvature surface then M is a Sasakian manifold.

Citations

• On circles and spheres in Riemannian geometry

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