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Totally real flat minimal surfaces in the hyperquadric

Authors:	Ling He Xiaoxiang Jiao Mingyan Li

Institution:	1. Center for Applied Mathematics, Tianjin University, Tianjin, China;2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China;3. School of Mathematical Sciences, Ocean University of China, Qingdao, China

Abstract:	In this paper, we study geometry of totally real minimal surfaces in the complex hyperquadric $Q_{N ? 2} $Q_{N-2}$$ , and obtain some characterizations of the harmonic sequence generated by these minimal immersions. For totally real flat surfaces that are minimal immersed in both $Q_{N ? 2} $Q_{N-2}$$ and $C P^{N ? 1} $\mathbb {C}P^{N-1}$$ , we determine them for $N = 4, 5, 6 $N=4, 5, 6$$ , and give a classification theorem when they are Clifford solutions.

Keywords:	Clifford solution complex hyperquadric minimal surfaces totally real