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  • Bulletin of the Australian Mathematical Society, Volume 81, Issue 1
  • January 2010, pp. 156-164

ON LEGENDRE CURVES IN CONTACT PSEUDO-HERMITIAN 3-MANIFOLDS

  • JI-EUN LEE (a1)
  • DOI: http://dx.doi.org/10.1017/S0004972709000872
  • Published online: 01 November 2009
Abstract
Abstract

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.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]K. Arslan and C. Ozgur , ‘Curves and surfaces of AW(k) type’, in: Geometry and Topology of Submanifolds, IX (Valenciennes/Lyon/Leuven, 1997) (World Scientific, River Edge, NJ, 1999), pp. 2126.

[2]C. Baikoussis and D. E. Blair , ‘On Legendre curves in contact 3-manifolds’, Geom. Dedicata 49 (1994), 135142.

[3]M. Barros and O. J. Garay , ‘On submanifolds with harmonic mean curvature’, Proc. Amer. Math. Soc. 123(8) (1995), 25452549.

[4]B.-Y. Chen , Total Mean Curvature and Submanifolds of Finite Type, Series in Pure Mathematics, 1 (World Scientific, Singapore, 1984).

[5]J. T. Cho , J. Inoguchi and J.-E. Lee , ‘Affine biharmonic submanifolds in three-dimensional pseudo-Hermitian geometry’, Abh. Math. Sem. Univ. Hamburg. 79 (2009), 113133.

[9]S. Tanno , ‘Variational problems on contact Riemannian manifolds’, Trans. Amer. Math. Soc. 314 (1989), 349379.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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