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Local rigidity of minimal surfaces in a hyperquadric \(Q_2\). (English) Zbl 1398.53068

Summary: In this paper, we study rigidity of a minimal immersion \(f\) from a surface \(M\) into a hyperquadric \(Q_2\). It is proved that except a case that \(f\) is totally geodesic, totally real with Gauss curvature \(K = 0\), then up to a rigidity, \(f\) is uniquely determined by the first fundamental form, the second fundamental form and Kähler angle.

MSC:

53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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