| Title:
|
Gap properties of harmonic maps and submanifolds (English) |
| Author:
|
Chen, Qun |
| Author:
|
Zhou, Zhen-Rong |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
41 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
59-69 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this article, we obtain a gap property of energy densities of harmonic maps from a closed Riemannian manifold to a Grassmannian and then, use it to Gaussian maps of some submanifolds to get a gap property of the second fundamental forms. (English) |
| Keyword:
|
Grassmannian |
| Keyword:
|
Gaussian map |
| Keyword:
|
mean curvature |
| Keyword:
|
the second fundamental form |
| MSC:
|
53C43 |
| MSC:
|
58E20 |
| idZBL:
|
Zbl 1112.58013 |
| idMR:
|
MR2142143 |
| . |
| Date available:
|
2008-06-06T22:45:08Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107935 |
| . |
| Reference:
|
[1] Chen W. H.: Geometry of Grassmannian manifolds as submanifolds.(in Chinese), Acta Math. Sinica 31(1) (1998), 46–53. MR 0951473 |
| Reference:
|
[2] Chen X. P.: Harmonic maps and Gaussian maps.(in Chinese), Chin. Ann. Math. 4A(4) (1983), 449–456. |
| Reference:
|
[3] Chern S. S., Goldberg S. I.: On the volume decreasing property of a class of real harmonic mappings.Amer. J. Math. 97(1) (1975), 133–147. Zbl 0303.53049, MR 0367860 |
| Reference:
|
[4] Chern S. S., doCarmo M., Kobayashi S.: Minimal submanifolds of a sphere with second fundamental form of constant length.Funct. Anal. Rel. Fields (1970), 59–75. MR 0273546 |
| Reference:
|
[5] Eells J., Lemaire L.: Selected topics on harmonic maps.Expository Lectures from the CBMS Regional Conf. held at Tulane Univ., Dec. 15–19, 1980. |
| Reference:
|
[6] Ruh E. A. Vilms J.: The tension field of the Gauss map.Trans. Amer. Math. Soc. 149 (1970), 569–573. MR 0259768 |
| Reference:
|
[7] Sealey H. C. J.: Harmonic maps of small energy.Bull. London Math. Soc. 13 (1981), 405–408. Zbl 0444.58009, MR 0631097 |
| Reference:
|
[8] Takahashi T.: Minimal immersions of Riemannian manifolds.J. Math. Soc. Japan. 18 (1966), 380–385. Zbl 0145.18601, MR 0198393 |
| Reference:
|
[9] Wu G. R., Chen W. H.: An inequality on matrix and its geometrical application.(in Chinese), Acta Math. Sinica 31(3) (1988), 348–355. MR 0963085 |
| Reference:
|
[10] Yano K., Kon M.: Structures on Manifolds.Series in Pure Math. 3 (1984), World Scientific. Zbl 0557.53001, MR 0794310 |
| . |
