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Brief Report Geometry of minimal surfaces in complex projective spaces

  • FU Jing-Chao ,
  • YU Yan
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  • College of Sciences, Northeast Dianli University, Jilin 132012, Jilin, China

Received date: 2011-10-08

  Revised date: 2012-03-12

  Online published: 2012-11-15

Abstract

We compute normal scaler curvature and obtain some basic relationships between Gaussian curvature, Kähler angle, length square of the second fundamental form, and normal scaler curvature. We also give some conditions for a conformal minimal sphere to have constant Kähler angle.

Cite this article

FU Jing-Chao , YU Yan . Brief Report Geometry of minimal surfaces in complex projective spaces[J]. Journal of University of Chinese Academy of Sciences, 2012 , (6) : 834 -840 . DOI: 10.7523/j.issn.2095-6134.2012.6.017

References

[1] Chern S S, Wolfson J G. Harmonic maps of the two-spheres in a complex Grassmann manifold[J]. Ann Math, 1987, 125: 301-335.
[2] Chern S S, Wolfson J G. Minimal surfaces by moving frames[J]. Amer J Math, 1983, 105: 59-83.
[3] Calabi E. Isometric embedding of complex manifolds[J]. Ann Math, 1953, 58: 1-23.
[4] Bolton J, Jensen G R, Rigoli M, et al. On conformal minimal immersions of S2 into CPn[J]. Math Ann, 1988, 279: 599-620.
[5] Jiao X X, Peng J G. Rigidity of holomorphic curves in complex Grassmann manifolds[J]. Math Ann, 2003, 327(3): 481-486.
[6] Uhlenbeck K. Harmonic maps into Lie groups (classical solutions of the chiral model)[J]. J Diff Geom, 1989, 30: 1-50.
[7] Jiao X X, Peng J G. Minimal 2-spheres in a complex projective space[J]. Diff Geom Appl, 2007, 25(5): 506-517.
[8] Eells J, Wood J C. Harmonic maps of surfaces to complex projective spaces[J]. Adv Math, 1983, 49: 217-263.
[9] Jiao X X, Peng J G. On some conformal minimal two-spheres in a complex projective space[J]. Quart J Math, 2010, 61(1): 87-101.
[10] Chen H X, Jiao X X. Conformal minimal immersions of in [J]. J Graduate University of Chinese Academic of Sciences, 2008, 25(4): 452-459.
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