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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.
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