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Submanifolds of complex quadrics and Gauss maps KU Leuven
The complex quadric and complex hyperbolic quadric are simply connected K\'ahler-Einstein manifolds. They can be constructed as K\'ahler submanifolds of the complex projective space and the complex anti-de Sitter space respectively, where the ambient spaces are equipped with the metric induced by the Hopf-fibration. The structure of the quadrics can be described in a very similar way and their curvature tensors are exactly opposite. In this ...