## 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

### Keywords:

unit spheres; Legendre curves; pseudo-Hermitian circles
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### References:

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