On Conformal Minimal Immersions of Two-Spheres in a Complex Hyperquadric with Parallel Second Fundamental Form

详细信息    查看全文

• 作者：Xiaoxiang Jiao ; Mingyan Li
• 关键词：Minimal two ; sphere ; Parallel second fundamental form ; Complex hyperquadric ; Classification ; Primary 53C42 ; 53C55
• 刊名：Journal of Geometric Analysis
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：26
• 期：1
• 页码：185-205
• 全文大小：525 KB
• 参考文献：1.Bahy-El-Dien, A., Wood, J.C.: The explicit construction of all harmonic two-spheres in \(G_2(R^n)\) . J. Reine Angew. Math. 398, 36–66 (1989)MATH MathSciNet
  2.Bolton, J., Jensen, G.R., Rigoli, M., Woodward, L.M.: On conformal minimal immersions of \(S^2\) into \(CP^n\) . Math. Ann. 279, 599–620 (1988)MATH MathSciNet CrossRef
  3.Burstall, F.E., Wood, J.C.: The construction of harmonic maps into complex Grassmannians. J. Diff. Geom. 23, 255–297 (1986)MATH MathSciNet
  4.Erdem, S., Wood, J.C.: On the construction of harmonic maps into a Grassmannian. J. Lond. Math. Soc. 28(2), 161–174 (1983)MATH MathSciNet CrossRef
  5.He, L., Jiao, X.-X.: Classification of all conformal minimal immersions of \(S^2\) in \(HP^n\) with parallel second fundamental form. Annali di Matematica. doi:10.​1007/​s10231-014-0420-8
  6.Jiao, X.-X.: On minimal two-spheres immersed in complex Grassmann manifolds with parallel second fundamental form. Monatsh. Math. 168, 381–401 (2012)MATH MathSciNet CrossRef
  7.Jiao, X.-X., Peng, J.-G.: On some conformal minimal two-spheres in a complex projective space. Quart. J. Math. 61(1), 87–101 (2010)MATH MathSciNet CrossRef
  8.Jiao, X.-X., Wang, J.: Minimal surfaces in a complex hyperquadric \(Q_2\) . Manuscripta Math. 140, 597–611 (2013)MATH MathSciNet CrossRef
  9.Nakagawa, H., Takagi, R.: On locally symmetric Kaehler submanifolds in a complex projective space. J. Math. Soc. Jpn. 28(4), 638–667 (1976)MATH MathSciNet CrossRef
  10.Uhlenbeck, K.: Harmonic maps into Lie groups (classical solutions of the chiral model). J. Diff. Geom. 30, 1–50 (1989)MATH MathSciNet
  11.Wolfson, J.G.: Harmonic maps of the two-sphere into the complex hyperquadric. J. Diff. Geom. 24, 141–152 (1986)MATH MathSciNet
  
• 作者单位：Xiaoxiang Jiao (1)
  Mingyan Li (1)
  
  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 101408, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Differential Geometry
  Convex and Discrete Geometry
  Fourier Analysis
  Abstract Harmonic Analysis
  Dynamical Systems and Ergodic Theory
  Global Analysis and Analysis on Manifolds
  
• 出版者：Springer New York
• ISSN：1559-002X

文摘

In this paper we determine all conformal minimal immersions of two-spheres in complex hyperquadric \(Q_n\) with parallel second fundamental form. Keywords Minimal two-sphere Parallel second fundamental form Complex hyperquadric Classification