Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-28T14:41:44.153Z Has data issue: false hasContentIssue false
  • English
  • Français

Minimal surfaces in ℂPn with constant curvature and Kähler angle

Published online by Cambridge University Press:  24 October 2008

J. Bolton  and
L. M. Woodward
J. Bolton
Affiliation:
Department of Mathematical Sciences, University of Durham, Science Laboratories, South Road, Durham, DH1 3LE
L. M. Woodward
Affiliation:
Department of Mathematical Sciences, University of Durham, Science Laboratories, South Road, Durham, DH1 3LE
Get access Rights & Permissions [Opens in a new window]

Extract

In [2] we used the theory of harmonic sequences to obtain a congruence theorem for minimal immersions of surfaces into ℂPn. In this paper we show how these ideas may be used to give a simplified and unified treatment of some results of Kenmotsu [9, 10], Bryant [4] and Ohnita [13].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 2 , September 1992 , pp. 287 - 296
Copyright
Copyright © Cambridge Philosophical Society 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Bando, S. and Ohnita, Y.. Minimal 2-spheres with constant curvature in Pn(ℂ). J. Math. Soc. Japan 39 (1987), 477–487.CrossRefGoogle Scholar
[2]Bolton, J. and WoodWard, L. M.. Congruence theorems for harmonic maps from a Riemann surface into CℂPn and Sn. J. Lond. Math. Soc., to appear.Google Scholar
[3]Bolton, J., Jensen, G. R., Rigoli, M. and Woodward, L. M.. On conformal minimal immersions of S 2 into ℂPn. Math. Ann. 279 (1988), 599–620.CrossRefGoogle Scholar
[4]Bryant, R. L.. Minimal surfaces of constant curvature in Sn. Trans. Amer. Math. Soc. 290 (1985), 259–271.Google Scholar
[5]Calabi, E.. Isometric embeddings of complex manifolds. Ann. of Math. 58 (1953), 1–23.CrossRefGoogle Scholar
[6]Chi, Q-S. and Zheng, Y.. Rigidity of pseudo-holomorphic curves of constant curvature in Grassmann manifolds. Trans. Amer. Math. Soc. 313 (1989), 393–406.CrossRefGoogle Scholar
[7]Din, A. M. and Zakrzewski, W. J.. General classical solutions in the ℂP n−1 model, Nuclear Phys. B. 174 (1980), 397–406.CrossRefGoogle Scholar
[8]Eells, J. and Wood, J. C.. Harmonic maps from surfaces to complex projective spaces. Adv. in Math. 49 (1983), 217–263.CrossRefGoogle Scholar
[9]Kenmotsu, K.. On a parametrisation of minimal immersions of ℝ2 into S 5. Tôhoku Math. J. 27 (1975), 83–90.CrossRefGoogle Scholar
[10]Kenmotsu, K.. On minimal immersions of ℝ2 into Pn(ℂ). J. Math. Soc. Japan 37 (1985), 665–682.CrossRefGoogle Scholar
[11]Lawson, H. B.. The Riemannian geometry of holomorphic curves. Proc. conf. on holomorphic mappings and minimal surfaces. Bol. Soc. Brasil Mat. 2 (1971), 45–62.CrossRefGoogle Scholar
[12]Ludden, G. D., Okumura, M. and Yano, K.. A totally real surface in ℂP 2 that is not totally geodesic. Proc. Amer. Math. Soc. 53 (1975), 186–190.Google Scholar
[13]Ohnita, Y.. Minimal surfaces with constant curvature and Kähler angle in complex space forms. Tsukuba J. Math. 13 (1989), 191–207.CrossRefGoogle Scholar
[14]Wolf, J. A.. Spaces of constant curvature (Publish or Perish, 1974).Google Scholar
[15]Wolfson, J. G.. Harmonic sequences and harmonic maps of surfaces into complex Grassman manifolds. J. Differential Geom. 27 (1988), 161–178.CrossRefGoogle Scholar