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SLANT CURVES IN CONTACT PSEUDO-HERMITIAN 3-MANIFOLDS

  • JONG TAEK CHO (a1) and JI-EUN LEE (a2) (a3)
Abstract
Abstract

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.

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Copyright
Corresponding author
For correspondence; e-mail: jtcho@chonnam.ac.kr
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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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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]M. Belkhelfa , F. Dillen and J. Inoguchi , ‘Surfaces with parallel second fundamental form in Binachi–Cartan–Vranceanu spaces’, in: PDE’s, Submanifolds and Affine Differential Geometry (Warsaw, 2000), Banach Center Publications, 57 (Polish Academy of Science, Warsaw, 2002), pp. 6787.

[3]D. E. Blair , Riemannian Geometry of Contact and Symplectic Manifolds, Progress in Mathematics, 203 (Birkhäuser, Boston, MA, 2002).

[4]R. Caddeo , S. Montaldo and C. Oniciuc , ‘Biharmonic submanifolds of S3’, Internat. J. Math. 12 (2001), 867876.

[5]R. Caddeo , S. Montaldo and P. Piu , ‘Biharmonic maps’, Contemp. Math. 288 (2001), 286290.

[7]B. Y. Chen and S. Ishikawa , ‘Biharmonic surfaces in pseudo-Euclidean spaces’, Mem. Fac. Kyushu Univ. Ser. A 45(2) (1991), 323347.

[10]J. T. Cho , J. Inoguchi and J.-E. Lee , ‘Biharmonic curves in 3-dimensional Sasakian space form’, Ann. Mat. Pura Appl. 186 (2007), 685701.

[11]J. Inoguchi , ‘Submanifolds with harmonic mean curvature in contact 3-manifold’, Colloq. Math. 100(6) (2004), 163179.

[15]S. Tanno , ‘Variantional 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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