On Veronese-Borůvka spheres

Katsuei Kenmotsu

Archivum Mathematicum (1997)

  • Volume: 033, Issue: 1-2, page 37-40
  • ISSN: 0044-8753

Abstract

top
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.

How to cite

top

Kenmotsu, Katsuei. "On Veronese-Borůvka spheres." Archivum Mathematicum 033.1-2 (1997): 37-40. <http://eudml.org/doc/248032>.

@article{Kenmotsu1997,
abstract = {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.},
author = {Kenmotsu, Katsuei},
journal = {Archivum Mathematicum},
keywords = {minimal immersions; constant curvature surfaces; harmonic maps; minimal immersions; constant curvature surfaces; harmonic maps},
language = {eng},
number = {1-2},
pages = {37-40},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On Veronese-Borůvka spheres},
url = {http://eudml.org/doc/248032},
volume = {033},
year = {1997},
}

TY - JOUR
AU - Kenmotsu, Katsuei
TI - On Veronese-Borůvka spheres
JO - Archivum Mathematicum
PY - 1997
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 033
IS - 1-2
SP - 37
EP - 40
AB - 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.
LA - eng
KW - minimal immersions; constant curvature surfaces; harmonic maps; minimal immersions; constant curvature surfaces; harmonic maps
UR - http://eudml.org/doc/248032
ER -

References

top
  1. S. Bando Y. Ohnita, Minimal 2-spheres with constant curvature in P n ( C ) , J. Math. Soc. Japan 39(1987), 477-487. (1987) MR0900981
  2. J. Bolton G. R. Jensen M. Rigoli L. M. Woodward, On conformal minimal immersions of S 2 into C P n , Math. Ann. 279(1988), 599-620. (1988) MR0926423
  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. (1928) 
  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. (1932) 
  5. O. Borůvka, Sur les surfaces representées par les fonctions sphériques de premiere espéce, J. Math. Pure et Appl. (1933) 337-383. (1933) 
  6. R. L. Bryant, Minimal surfaces of constant curvature in S n , Trans. Amer. Math. Soc. 290(1985), 259-271. (1985) MR0787964
  7. E. Calabi, Minimal immersions of surfaces in euclidean spheres, J. Diff. Geo. 1(1967), 111-125. (1967) Zbl0171.20504MR0233294
  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. (1989) MR0992602
  9. Q-S. Chi G. R. Jensen R. Liao, Isoparametric Functions and Flat Minimal Tori in C P 2 , Proc. Amer. Math. Soc. 123(1995), 2849-2854. (1995) MR1260163
  10. K. Kenmotsu, On minimal immersions of R 2 into S n , Jour. of Math. Soc. Japan 28(1976), 182-191. (1976) MR0405218
  11. K. Kenmotsu, Minimal surfaces with constant curvature in 4-dimensional space forms, Proc. Amer. Math. Soc. 89(1983), 133-138. (1983) Zbl0531.53046MR0706526
  12. K. Kenmotsu, On minimal immersions of R 2 into P n ( C ) , Jour. of Math. Soc. Japan 37(1985), 663-680. (1985) MR0806307
  13. K. Kenmotsu K. Masuda, On the Kähler angles of minimal surfaces of constant curvature in C P 2 , in preparation. 
  14. G. Ludden M. Okumura K. Yano, A totally real surface in C P 2 that is not totally geodesic, Proc. Amer. Math. Soc. 53(1975), 186-190. (1975) MR0380683
  15. T. Ogata, U.Simon’s conjectures on minimal submanifolds in a sphere, Bull. Yamagata Univ. 11(1987), 345-350. (1987) MR0879861
  16. Y. Ohnita, Minimal surfaces with constant curvature and Kähler angle in complex space forms, Tsukuba J. Math. 13(1989), 191-207. (1989) Zbl0678.53055MR1003602
  17. J. Simons, Minimal varieties in riemannian manifolds, Ann. Math. 88(1968), 62-105. (1968) Zbl0181.49702MR0233295
  18. N. Wallach, Extension of locally defined minimal immersions of spheres into spheres, Arch. Math. 21(1970), 210-213. (1970) MR0271878

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.