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arXiv · 1912.00165

Characterization of 3D Sasakian manifold from magnetic Hopf surfaces

Satsuki Matsuno
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Abstract

In a three-dimensional Riemannian manifold M that admits a unit Killing vector field $\xi$, we regard $\xi$ as a magnetic vector field. A magnetic Hopf surface is a surface obtained by Lie dragging the magnetic curve with $\xi$. 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.

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Satsuki Matsuno. 2019-11-30. Characterization of 3D Sasakian manifold from magnetic Hopf surfaces. https://arxiv.org/abs/1912.00165

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