| Title:
|
Submanifolds with harmonic mean curvature in pseudo-Hermitian geometry (English) |
| Author:
|
Inoguchi, Jun-ichi |
| Author:
|
Lee, Ji-Eun |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
48 |
| Issue:
|
1 |
| Year:
|
2012 |
| Pages:
|
15-26 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We classify Hopf cylinders with proper mean curvature vector field in Sasakian 3-manifolds with respect to the Tanaka-Webster connection. (English) |
| Keyword:
|
pseudo-hermitian mean curvature vector fields |
| Keyword:
|
proper mean curvature |
| Keyword:
|
biharmonic submanifolds |
| Keyword:
|
biminimal immersions |
| MSC:
|
58E20 |
| idMR:
|
MR2915846 |
| DOI:
|
10.5817/AM2012-1-15 |
| . |
| Date available:
|
2012-03-15T18:06:19Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142088 |
| . |
| Reference:
|
[1] Barros, M., Garay, O. J.: On submanifolds with harmonic mean curvature.Proc. Amer. Math. Soc. 123 (1995), 2545–2549. Zbl 0827.53015, MR 1254831, 10.1090/S0002-9939-1995-1254831-7 |
| Reference:
|
[2] Chen, B. Y.: Some classification theorems for submanifolds in Minkowski space–time.Arch. Math. (Basel) 62 (1994), 177–182. Zbl 0816.53035, MR 1255641, 10.1007/BF01198672 |
| Reference:
|
[3] Chen, B. Y.: Submanifolds in de Sitter space–time satisfying $\Delta H = \lambda H$.Israel J. Math. 91 (1995), 373–391. Zbl 0873.53041, MR 1348323 |
| Reference:
|
[4] Chen, B. Y.: Report on submanifolds of finite type.Soochow J. Math. 22 (1996), 117–337. Zbl 0867.53001, MR 1391469 |
| Reference:
|
[5] Cho, J. T., Inoguchi, J., Lee, J.-E.: Affine biharmonic submanifolds in 3–dimensional pseudo–Hermitian geometry.Abh. Math. Sem. Univ. Hamburg 79 (2009), 113–133. Zbl 1180.58010, MR 2541346, 10.1007/s12188-008-0014-8 |
| Reference:
|
[6] Defever, F.: Hypersurfaces of $E^4$ satisfying $\Delta H = \lambda H$.Michigan Math. J. 44 (1997), 355–364. MR 1460420 |
| Reference:
|
[7] Defever, F.: Hypersurfaces of $E^4$ with harmonic mean curvature vector.Math. Nachr. 196 (1998), 61–69. MR 1657990, 10.1002/mana.19981960104 |
| Reference:
|
[8] Defever, F.: Theory of semisymmetric conformally flat and biharmonic submanifolds.Balkan J. Geom. Appl. 4 (1999), 19–30. Zbl 0980.53006, MR 1751643 |
| Reference:
|
[9] Dimitric, I.: Submanifolds of $E^m$ with harmonic mean curvature vector.Bull. Inst. Math. Acad. Sinica 20 (1992), 53–65. MR 1166218 |
| Reference:
|
[10] Ferrández, A., Lucas, P., Meroño, M. A.: Biharmonic Hopf cylinders.Rocky Mountain J. Math. 28 (1998), 957–975. MR 1656996, 10.1216/rmjm/1181071748 |
| Reference:
|
[11] Garay, O. J.: A classification of certain 3–dimensional conformally flat Euclidean hypersurfaces.Pacific J. Math. 162 (1994), 13–25. Zbl 0791.53026, MR 1247141, 10.2140/pjm.1994.162.13 |
| Reference:
|
[12] Hasanis, Th., Vlachos, Th.: Hypersurfaces in $E^4$ with harmonic mean curvature vector field.Math. Nachr. 172 (1995), 145–169. MR 1330627, 10.1002/mana.19951720112 |
| Reference:
|
[13] Inoguchi, J.: Submanifolds with harmonic mean curvature vector field in contact 3-manifolds.Colloq. Math. 100 (2004), 163–179. Zbl 1076.53065, MR 2107514, 10.4064/cm100-2-2 |
| Reference:
|
[14] Inoguchi, J.: Biminimal submanifolds in 3–dimensional contact manifolds.Balkan J. Geom. Appl. 12 (1) (2007), 56–67. MR 2321968 |
| Reference:
|
[15] Inoguchi, J., Lee, J.-E.: Almost contact curves in normal almost contact $3$-manifolds.submitted. |
| Reference:
|
[16] Inoguchi, J., Lee, J.-E.: Biminimal curves in $2$–dimensional space forms.submitted. |
| Reference:
|
[17] Lee, J.-E.: On Legendre curves in contact pseudo–Hermitian 3–manifolds.Bull. Austral. Math. Soc. 81 (1) (2010), 156–164. Zbl 1185.53048, MR 2584930, 10.1017/S0004972709000872 |
| Reference:
|
[18] Loubeau, E., Montaldo, S.: Biminimal immersions.Proc. Edinburgh Math. Soc. (2) 51 (2008), 421–437. Zbl 1144.58010, MR 2465916 |
| Reference:
|
[19] Ogiue, K.: On fiberings of almost contact manifolds.Kōdai Math. Sem. Rep. 17 (1965), 53–62. Zbl 0136.18101, MR 0178428, 10.2996/kmj/1138845019 |
| Reference:
|
[20] O’Neill, B.: The fundamental equations of a submersion.Michigan Math. J. 13 (1966), 459–469. MR 0200865, 10.1307/mmj/1028999604 |
| Reference:
|
[21] Tanaka, N.: On non–degenerate real hypersurfaces, graded Lie algebras and Cartan connections.Japan. J. Math. (N.S.) 2 (1) (1976), 131–190. Zbl 0346.32010, MR 0589931 |
| Reference:
|
[22] Tanno, S.: Variational problems on contact Riemannian manifolds.Trans. Amer. Math. Soc. 314 (1989), 349–379. Zbl 0677.53043, MR 1000553, 10.1090/S0002-9947-1989-1000553-9 |
| Reference:
|
[23] Webster, S. M.: Pseudohermitian structures on a real hypersurface.J. Differential Geom. 13 (1978), 25–41. MR 0520599 |
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