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.
@article{107595, author = {Katsuei Kenmotsu}, title = {On Veronese-Bor\r uvka spheres}, journal = {Archivum Mathematicum}, volume = {033}, year = {1997}, pages = {37-40}, zbl = {0910.53002}, mrnumber = {1464299}, language = {en}, url = {http://dml.mathdoc.fr/item/107595} }
Kenmotsu, Katsuei. On Veronese-Borůvka spheres. Archivum Mathematicum, Tome 033 (1997) pp. 37-40. http://gdmltest.u-ga.fr/item/107595/
Minimal 2-spheres with constant curvature in $P_{n}(C)$, J. Math. Soc. Japan 39(1987), 477-487. (1987) | MR 0900981
On conformal minimal immersions of $S^{2}$ into $CP^{n}$, Math. Ann. 279(1988), 599-620. (1988) | MR 0926423
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. (1928)
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. (1932)
Sur les surfaces representées par les fonctions sphériques de premiere espéce, J. Math. Pure et Appl. (1933) 337-383. (1933)
Minimal surfaces of constant curvature in $S^{n}$, Trans. Amer. Math. Soc. 290(1985), 259-271. (1985) | MR 0787964
Minimal immersions of surfaces in euclidean spheres, J. Diff. Geo. 1(1967), 111-125. (1967) | MR 0233294 | Zbl 0171.20504
Rigidity of pseudo-holomorphic curves of constant curvature in Grassmann manifolds, Trans. Amer. Math. Soc. 313(1989), 393-406. (1989) | MR 0992602
Isoparametric Functions and Flat Minimal Tori in $CP^{2}$, Proc. Amer. Math. Soc. 123(1995), 2849-2854. (1995) | MR 1260163
On minimal immersions of $R^{2}$ into $S^{n}$, Jour. of Math. Soc. Japan 28(1976), 182-191. (1976) | MR 0405218
Minimal surfaces with constant curvature in 4-dimensional space forms, Proc. Amer. Math. Soc. 89(1983), 133-138. (1983) | MR 0706526 | Zbl 0531.53046
On minimal immersions of $R^{2}$ into $P^{n}(C)$, Jour. of Math. Soc. Japan 37(1985), 663-680. (1985) | MR 0806307
On the Kähler angles of minimal surfaces of constant curvature in $CP^{2}$, in preparation.
A totally real surface in $CP^{2}$ that is not totally geodesic, Proc. Amer. Math. Soc. 53(1975), 186-190. (1975) | MR 0380683
U.Simon’s conjectures on minimal submanifolds in a sphere, Bull. Yamagata Univ. 11(1987), 345-350. (1987) | MR 0879861
Minimal surfaces with constant curvature and Kähler angle in complex space forms, Tsukuba J. Math. 13(1989), 191-207. (1989) | MR 1003602 | Zbl 0678.53055
Minimal varieties in riemannian manifolds, Ann. Math. 88(1968), 62-105. (1968) | MR 0233295 | Zbl 0181.49702
Extension of locally defined minimal immersions of spheres into spheres, Arch. Math. 21(1970), 210-213. (1970) | MR 0271878