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.


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
Full Text: DOI


[1] Cho, Bull. Austral. Math. Soc. 74 pp 359– (2006)
[2] DOI: 10.1007/s10231-006-0026-x · Zbl 1141.53060
[3] DOI: 10.2206/kyushumfs.45.323 · Zbl 0757.53009
[4] Cartan, Leçons sur la géométrie des espaces de Riemann (1946)
[5] Caddeo, Contemp. Math. 288 pp 286– (2001)
[6] Webster, J. Differential Geom. 13 pp 25– (1978)
[7] DOI: 10.1142/S0129167X01001027 · Zbl 1111.53302
[8] Blair, Riemannian Geometry of Contact and Symplectic Manifolds (2002)
[9] DOI: 10.2307/2001446 · Zbl 0677.53043
[10] Bianchi, Lezioni di Geometrie Differenziale (1894)
[11] Tanaka, Japan J. Math. 2 pp 131– (1976)
[12] DOI: 10.4064/bc57-0-5
[13] Tamura, Comment. Math. Univ. St. Pauli 52 pp 117– (2003)
[14] Kobayashi, Transformation Groups in Differential Geometry (1972) · Zbl 0246.53031
[15] DOI: 10.4064/cm100-2-2 · Zbl 1076.53065
[16] Cho, J. Korean Math. Soc. 43 pp 1019– (2006)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.