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ON LEGENDRE CURVES IN CONTACT PSEUDO-HERMITIAN 3-MANIFOLDS
Part of
- Variational problems in infinite-dimensional spaces
JI-EUN LEE
Journal:

Bulletin of the Australian Mathematical Society / Volume 81 / Issue 1 / February 2010

Published online by Cambridge University Press:

05 November 2009, pp. 156-164

Print publication:

February 2010
- Article
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We find necessary and sufficient conditions for a Legendre curve in a Sasakian manifold to have: (i) a pseudo-Hermitian parallel mean curvature vector field; (ii) a pseudo-Hermitian proper mean curvature vector field in the normal bundle.

SLANT CURVES IN CONTACT PSEUDO-HERMITIAN 3-MANIFOLDS
Part of
- Fairly general properties
- Global differential geometry
JONG TAEK CHO, JI-EUN LEE
Journal:

Bulletin of the Australian Mathematical Society / Volume 78 / Issue 3 / December 2008

Published online by Cambridge University Press:

01 December 2008, pp. 383-396

Print publication:

December 2008
- Article
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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.