Submanifolds with harmonic mean curvature in pseudo-Hermitian geometry

Jun-ichi Inoguchi; Ji-Eun Lee

Archivum Mathematicum (2012)

  • Volume: 048, Issue: 1, page 15-26
  • ISSN: 0044-8753

Abstract

top
We classify Hopf cylinders with proper mean curvature vector field in Sasakian 3-manifolds with respect to the Tanaka-Webster connection.

How to cite

top

Inoguchi, Jun-ichi, and Lee, Ji-Eun. "Submanifolds with harmonic mean curvature in pseudo-Hermitian geometry." Archivum Mathematicum 048.1 (2012): 15-26. <http://eudml.org/doc/246111>.

@article{Inoguchi2012,
abstract = {We classify Hopf cylinders with proper mean curvature vector field in Sasakian 3-manifolds with respect to the Tanaka-Webster connection.},
author = {Inoguchi, Jun-ichi, Lee, Ji-Eun},
journal = {Archivum Mathematicum},
keywords = {pseudo-hermitian mean curvature vector fields; proper mean curvature; biharmonic submanifolds; biminimal immersions; pseudo-Hermitian; mean curvature vector field; proper mean curvature; biharmonic submanifold; biminimal immersion},
language = {eng},
number = {1},
pages = {15-26},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Submanifolds with harmonic mean curvature in pseudo-Hermitian geometry},
url = {http://eudml.org/doc/246111},
volume = {048},
year = {2012},
}

TY - JOUR
AU - Inoguchi, Jun-ichi
AU - Lee, Ji-Eun
TI - Submanifolds with harmonic mean curvature in pseudo-Hermitian geometry
JO - Archivum Mathematicum
PY - 2012
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 048
IS - 1
SP - 15
EP - 26
AB - We classify Hopf cylinders with proper mean curvature vector field in Sasakian 3-manifolds with respect to the Tanaka-Webster connection.
LA - eng
KW - pseudo-hermitian mean curvature vector fields; proper mean curvature; biharmonic submanifolds; biminimal immersions; pseudo-Hermitian; mean curvature vector field; proper mean curvature; biharmonic submanifold; biminimal immersion
UR - http://eudml.org/doc/246111
ER -

References

top
  1. Barros, M., Garay, O. J., 10.1090/S0002-9939-1995-1254831-7, Proc. Amer. Math. Soc. 123 (1995), 2545–2549. (1995) Zbl0827.53015MR1254831DOI10.1090/S0002-9939-1995-1254831-7
  2. Chen, B. Y., 10.1007/BF01198672, Arch. Math. (Basel) 62 (1994), 177–182. (1994) Zbl0816.53035MR1255641DOI10.1007/BF01198672
  3. Chen, B. Y., Submanifolds in de Sitter space–time satisfying Δ H = λ H , Israel J. Math. 91 (1995), 373–391. (1995) Zbl0873.53041MR1348323
  4. Chen, B. Y., Report on submanifolds of finite type, Soochow J. Math. 22 (1996), 117–337. (1996) Zbl0867.53001MR1391469
  5. Cho, J. T., Inoguchi, J., Lee, J.-E., 10.1007/s12188-008-0014-8, Abh. Math. Sem. Univ. Hamburg 79 (2009), 113–133. (2009) Zbl1180.58010MR2541346DOI10.1007/s12188-008-0014-8
  6. Defever, F., Hypersurfaces of E 4 satisfying Δ H = λ H , Michigan Math. J. 44 (1997), 355–364. (1997) MR1460420
  7. Defever, F., 10.1002/mana.19981960104, Math. Nachr. 196 (1998), 61–69. (1998) MR1657990DOI10.1002/mana.19981960104
  8. Defever, F., Theory of semisymmetric conformally flat and biharmonic submanifolds, Balkan J. Geom. Appl. 4 (1999), 19–30. (1999) Zbl0980.53006MR1751643
  9. Dimitric, I., Submanifolds of E m with harmonic mean curvature vector, Bull. Inst. Math. Acad. Sinica 20 (1992), 53–65. (1992) MR1166218
  10. Ferrández, A., Lucas, P., Meroño, M. A., 10.1216/rmjm/1181071748, Rocky Mountain J. Math. 28 (1998), 957–975. (1998) MR1656996DOI10.1216/rmjm/1181071748
  11. Garay, O. J., 10.2140/pjm.1994.162.13, Pacific J. Math. 162 (1994), 13–25. (1994) Zbl0791.53026MR1247141DOI10.2140/pjm.1994.162.13
  12. Hasanis, Th., Vlachos, Th., 10.1002/mana.19951720112, Math. Nachr. 172 (1995), 145–169. (1995) MR1330627DOI10.1002/mana.19951720112
  13. Inoguchi, J., 10.4064/cm100-2-2, Colloq. Math. 100 (2004), 163–179. (2004) Zbl1076.53065MR2107514DOI10.4064/cm100-2-2
  14. Inoguchi, J., Biminimal submanifolds in 3–dimensional contact manifolds, Balkan J. Geom. Appl. 12 (1) (2007), 56–67. (2007) MR2321968
  15. Inoguchi, J., Lee, J.-E., Almost contact curves in normal almost contact 3 -manifolds, submitted. 
  16. Inoguchi, J., Lee, J.-E., Biminimal curves in 2 –dimensional space forms, submitted. 
  17. Lee, J.-E., 10.1017/S0004972709000872, Bull. Austral. Math. Soc. 81 (1) (2010), 156–164. (2010) Zbl1185.53048MR2584930DOI10.1017/S0004972709000872
  18. Loubeau, E., Montaldo, S., Biminimal immersions, Proc. Edinburgh Math. Soc. (2) 51 (2008), 421–437. (2008) Zbl1144.58010MR2465916
  19. Ogiue, K., 10.2996/kmj/1138845019, Kōdai Math. Sem. Rep. 17 (1965), 53–62. (1965) Zbl0136.18101MR0178428DOI10.2996/kmj/1138845019
  20. O’Neill, B., 10.1307/mmj/1028999604, Michigan Math. J. 13 (1966), 459–469. (1966) MR0200865DOI10.1307/mmj/1028999604
  21. Tanaka, N., On non–degenerate real hypersurfaces, graded Lie algebras and Cartan connections, Japan. J. Math. (N.S.) 2 (1) (1976), 131–190. (1976) Zbl0346.32010MR0589931
  22. Tanno, S., 10.1090/S0002-9947-1989-1000553-9, Trans. Amer. Math. Soc. 314 (1989), 349–379. (1989) Zbl0677.53043MR1000553DOI10.1090/S0002-9947-1989-1000553-9
  23. Webster, S. M., Pseudohermitian structures on a real hypersurface, J. Differential Geom. 13 (1978), 25–41. (1978) MR0520599

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.