| Title:
|
On Veronese-Borůvka spheres (English) |
| Author:
|
Kenmotsu, K. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
33 |
| Issue:
|
1 |
| Year:
|
1997 |
| Pages:
|
37-40 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, history of reserches for minimal immersions from constant Gaussian curvature 2-manifolds into space forms is explained with special emphasis of works of O. Borůvka. Then recent results for the corresponding probrem to classify minimal immersions of such surfaces in complex space forms are discussed. (English) |
| Keyword:
|
minimal immersions |
| Keyword:
|
constant curvature surfaces |
| Keyword:
|
harmonic maps |
| MSC:
|
53A10 |
| MSC:
|
53C42 |
| idZBL:
|
Zbl 0910.53002 |
| idMR:
|
MR1464299 |
| . |
| Date available:
|
2008-06-06T21:32:21Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107595 |
| . |
| Reference:
|
[1] S. Bando Y. Ohnita: Minimal 2-spheres with constant curvature in $P_{n}(C)$.J. Math. Soc. Japan 39(1987), 477-487. MR 0900981 |
| Reference:
|
[2] J. Bolton G. R. Jensen M. Rigoli L. M. Woodward: On conformal minimal immersions of $S^{2}$ into $CP^{n}$.Math. Ann. 279(1988), 599-620. MR 0926423 |
| Reference:
|
[3] O. Borůvka: Sur une classe de surfaces minima plongées dans un espace á quatre dimensions á courbure constante.Bull. Intern. de l’Acad. Tech. des Sci. Prague 29(1928), 256-277. |
| Reference:
|
[4] O. Borůvka: Recherches sur la courbure des surfaces dans des espaces à n dimensions à courbure constante I.Publ. de la Fac. des Sci. de L’universite Masaryk (1932) 2-22. |
| Reference:
|
[5] O. Borůvka: Sur les surfaces representées par les fonctions sphériques de premiere espéce.J. Math. Pure et Appl. (1933) 337-383. |
| Reference:
|
[6] R. L. Bryant: Minimal surfaces of constant curvature in $S^{n}$.Trans. Amer. Math. Soc. 290(1985), 259-271. MR 0787964 |
| Reference:
|
[7] E. Calabi: Minimal immersions of surfaces in euclidean spheres.J. Diff. Geo. 1(1967), 111-125. Zbl 0171.20504, MR 0233294 |
| Reference:
|
[8] Q-S. Chi Y. Zheng: Rigidity of pseudo-holomorphic curves of constant curvature in Grassmann manifolds.Trans. Amer. Math. Soc. 313(1989), 393-406. MR 0992602 |
| Reference:
|
[9] Q-S. Chi G. R. Jensen R. Liao: Isoparametric Functions and Flat Minimal Tori in $CP^{2}$.Proc. Amer. Math. Soc. 123(1995), 2849-2854. MR 1260163 |
| Reference:
|
[10] K. Kenmotsu: On minimal immersions of $R^{2}$ into $S^{n}$.Jour. of Math. Soc. Japan 28(1976), 182-191. MR 0405218 |
| Reference:
|
[11] K. Kenmotsu: Minimal surfaces with constant curvature in 4-dimensional space forms.Proc. Amer. Math. Soc. 89(1983), 133-138. Zbl 0531.53046, MR 0706526 |
| Reference:
|
[12] K. Kenmotsu: On minimal immersions of $R^{2}$ into $P^{n}(C)$.Jour. of Math. Soc. Japan 37(1985), 663-680. MR 0806307 |
| Reference:
|
[13] K. Kenmotsu K. Masuda: On the Kähler angles of minimal surfaces of constant curvature in $CP^{2}$.in preparation. |
| Reference:
|
[14] G. Ludden M. Okumura K. Yano: A totally real surface in $CP^{2}$ that is not totally geodesic.Proc. Amer. Math. Soc. 53(1975), 186-190. MR 0380683 |
| Reference:
|
[15] T. Ogata: U.Simon’s conjectures on minimal submanifolds in a sphere.Bull. Yamagata Univ. 11(1987), 345-350. MR 0879861 |
| Reference:
|
[16] Y. Ohnita: Minimal surfaces with constant curvature and Kähler angle in complex space forms.Tsukuba J. Math. 13(1989), 191-207. Zbl 0678.53055, MR 1003602 |
| Reference:
|
[17] J. Simons: Minimal varieties in riemannian manifolds.Ann. Math. 88(1968), 62-105. Zbl 0181.49702, MR 0233295 |
| Reference:
|
[18] N. Wallach: Extension of locally defined minimal immersions of spheres into spheres.Arch. Math. 21(1970), 210-213. MR 0271878 |
| . |
