Minimal Surfaces in \(\mathbb{S}^{2} \times\mathbb{S}^{2}\)

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• 作者：Francisco Torralbo (1)
  Francisco Urbano (1)
  
  1. Departamento de Geometr铆a y Topolog铆a ; Universidad de Granada ; 18071 ; Granada ; Spain
  
• 关键词：Surfaces ; Minimal ; Complex surfaces ; 53C42 ; 53C40
• 刊名：Journal of Geometric Analysis
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：25
• 期：2
• 页码：1132-1156
• 全文大小：375 KB
• 参考文献：1. Asperti, A.C., Ferus, D., Rodr铆guez, L. (1982) Surfaces with nonzero normal curvature. Rend. Sci. Fis. Mat. Lincei 73: pp. 109-115
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  15. Torralbo, F., Urbano, F. (2012) Surfaces with parallel mean curvature vector in $\mathbb {S}^{2} \times \mathbb {S}^{2}$ and $\mathbb {H}^{2} \times \mathbb {H}^{2}$. Trans. Am. Math. Soc. 364: pp. 785-813 CrossRef
  16. Torralbo, F., Urbano, F.: Compact stable minimal submanifolds. To appear in Proc. Am. Math. Soc.
  17. Wolfson, J.G. (1989) Minimal surfaces in K盲hler surfaces and Ricci curvature. J. Differ. Geom. 29: pp. 281-294
  
• 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

A general study of minimal surfaces of the Riemannian product of two spheres \(\mathbb {S}^{2}\times \mathbb {S}^{2}\) is tackled. We establish a local correspondence between (non-complex) minimal surfaces of \(\mathbb {S}^{2} \times \mathbb {S}^{2}\) and a certain pair of minimal surfaces of the sphere \(\mathbb {S}^{3}\) . This correspondence also allows us to link minimal surfaces in \(\mathbb{S}^{3}\) and in the Riemannian product \(\mathbb {S}^{2} \times \mathbb {R}\) . Some rigidity results for compact minimal surfaces are also obtained.