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In this paper, we study geometry of totally real minimal surfaces in thecomplex hyperquadric $Q_{N-2}$, and obtain some characterizations of theharmonic sequence generated by these minimal immersions. For totally real flatsurfaces that are minimal in both $Q_{N-2}$ and $\mathbb{C}P^{N-1}$, wedetermine them for $N=4, 5, 6$, and give a classification theorem when they areClifford solutions.

Totally Real Flat Minimal Surface in Hyperquadric