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SLANT CURVES IN CONTACT PSEUDO-HERMITIAN 3-MANIFOLDS

Part of: Fairly general properties Global differential geometry

Published online by Cambridge University Press:  01 December 2008

JONG TAEK CHO  and
JI-EUN LEE
JONG TAEK CHO*
Affiliation:
Department of Mathematics, CNU The Institute of Basic Science, Chonnam National University, Gwangju 500–757, Korea (email: jtcho@chonnam.ac.kr)
JI-EUN LEE
Affiliation:
National Institute for Mathematical Sciences, 385-16 Doryong-dong, Yuseong-gu Daejeon 305-340, Korea (email: jelee@nims.re.kr) Department of Mathematics, Graduate School, Chonnam National University, Gwangju 500–757, Korea (email: jelee@chonnam.ac.kr)
*
✉For correspondence; e-mail: jtcho@chonnam.ac.kr
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Abstract

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By using the pseudo-Hermitian connection (or Tanaka–Webster connection) , we construct the parametric equations of Legendre pseudo-Hermitian circles (whose -geodesic curvature is constant and -geodesic torsion is zero) in S3. In fact, it is realized as a Legendre curve satisfying the -Jacobi equation for the -geodesic vector field along it.

Keywords

unit spheresLegendre curvespseudo-Hermitian circles

MSC classification

Secondary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C43: Differential geometric aspects of harmonic maps 54D10: Lower separation axioms ($T_0$--$T_3$, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 78 , Issue 3 , December 2008 , pp. 383 - 396
Copyright
Copyright © 2009 Australian Mathematical Society

Footnotes

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

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