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Slant curves in contact pseudo-Hermitian 3-manifolds. (English) Zbl 1158.53062

Summary: By using the pseudo-Hermitian connection (or Tanaka-Webster connection) \(\widehat \nabla \), we construct the parametric equations of Legendre pseudo-Hermitian circles (whose \(\widehat \nabla \)-geodesic curvature \(\widehat \kappa \) is constant and \(\widehat \nabla \)-geodesic torsion \(\widehat \tau \) is zero) in \(S^3\). In fact, it is realized as a Legendre curve satisfying the \(\widehat \nabla \)-Jacobi equation for the \(\widehat \nabla \)-geodesic vector field along it.

MSC:

53D15 Almost contact and almost symplectic manifolds
53C43 Differential geometric aspects of harmonic maps
54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.)
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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References:

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