Bulletin of the Australian Mathematical Society

Research Article

SLANT CURVES IN CONTACT PSEUDO-HERMITIAN 3-MANIFOLDS

JONG TAEK CHOa1 c1 and JI-EUN LEEa2a3

a1 Department of Mathematics, CNU The Institute of Basic Science, Chonnam National University, Gwangju 500–757, Korea (email: jtcho@chonnam.ac.kr)

a2 National Institute for Mathematical Sciences, 385-16 Doryong-dong, Yuseong-gu Daejeon 305-340, Korea (email: jelee@nims.re.kr)

a3 Department of Mathematics, Graduate School, Chonnam National University, Gwangju 500–757, Korea (email: jelee@chonnam.ac.kr)

Abstract

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 S3. In fact, it is realized as a Legendre curve satisfying the $\widehat \nabla $-Jacobi equation for the $\widehat \nabla $-geodesic vector field along it.

(Received January 14 2008)

2000 Mathematics subject classification

  • 53C25;
  • 53C43;
  • 54D10

Keywords and phrases

  • unit spheres;
  • Legendre curves;
  • pseudo-Hermitian circles

Correspondence:

c1 For correspondence; e-mail: jtcho@chonnam.ac.kr

Footnotes

The second author was supported by the Korea Research Council of Fundamental Science & Technology (KRCF), Grant No. C-RESEARCH-2006-11-NIMS.