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The generalized Gauss map of an immersed oriented surface M in Λ 4 is the map which associates to each point of M its oriented tangent plane in G 2A9 the Grassmannian of oriented planes in R\ The Grassmannian G 2)4 is naturally identified with Q 2 , the complex hyperquadric j[zi, z 2 , z 3 , z 4 ] Σ zl=θϊ in P 3 (C) . The normalized Fubini-Study metric on P B (C) with holomorphic curvature 2 induces an invariant metric on Q 2 = G 2A , which corresponds exactly to the metric on the canonicaldoi:10.2140/pjm.1982.102.9 fatcat:kkdwdapz6bhezficy6rb2cflem