Abstract
We present new steady Euler solutions on the (round) 3-sphere, that bifurcate from an ansatz proposed in [11], showing that these previously known solutions are not isolated. We also extend this ansatz to any Sasakian 3-manifold, such as the Heisenberg group and \(SL(2, \mathbb {R})\).
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Here by pull-back of a vector field X through some mapping \(\varphi \) we mean \((\varphi ^* X^\flat )^\sharp \) and the pull-back of a function f on the codomain is \(f\circ \varphi \) defined on the domain of \(\varphi \).
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Slobodeanu, R. Steady Euler Flows on the 3-Sphere and Other Sasakian 3-Manifolds. Qual. Theory Dyn. Syst. 20, 5 (2021). https://doi.org/10.1007/s12346-020-00440-y
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DOI: https://doi.org/10.1007/s12346-020-00440-y