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Minimal surfaces in the complex hyperquadric $ Q_2$ II


Authors: Jun Wang and Xiaowei Xu
Journal: Proc. Amer. Math. Soc. 143 (2015), 2693-2703
MSC (2010): Primary 53C42, 53C55
DOI: https://doi.org/10.1090/S0002-9939-2015-12479-3
Published electronically: January 21, 2015
MathSciNet review: 3326047
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Abstract: In this paper, minimal surfaces with parallel second fundamental form in $ Q_2$ are classified, which are uniquely determined up to a rigidity motion. It is also proved that minimal surfaces in $ Q_2$ with constant Gauss curvature and constant normal curvature are totally geodesic.


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Additional Information

Jun Wang
Affiliation: School of Mathematics Sciences and Institute of Mathematics, Nanjing Normal University, Nanjing 210023, People’s Republic of China
Email: wangjun706@mails.ucas.ac.cn

Xiaowei Xu
Affiliation: School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, Anhui province, People’s Republic of China; and Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences, Hefei, 230026, Anhui, People’s Republic of China
Email: xwxu09@ustc.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-2015-12479-3
Keywords: Minimal surfaces, constant curvature, K\"ahler angle, totally geodesic
Received by editor(s): October 8, 2013
Received by editor(s) in revised form: January 27, 2014
Published electronically: January 21, 2015
Additional Notes: Xiaowei Xu served as corresponding author for this paper.
Communicated by: Chuu-Lian Terng
Article copyright: © Copyright 2015 American Mathematical Society