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Antonio J. di Scala, Minimal Immersions of Kähler Manifolds into Euclidean Spaces, Bulletin of the London Mathematical Society, Volume 35, Issue 6, November 2003, Pages 825–827, https://doi.org/10.1112/S0024609303002492
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Abstract
It is proved here that a minimal isometric immersion of a Kähler-Einstein or homogeneous Kähler-manifold into an Euclidean space must be totally geodesic. As an application, it is shown that an open subset of the real hyperbolic plane R H2 cannot be minimally immersed into the Euclidean space. As another application, a proof is given that if an irreducible Kähler manifold is minimally immersed in a Euclidean space, then its restricted holonomy group must be U ( n ), where n = dim CM . 2000 Mathematics Subject Classification 53B25 (primary); 53C42 (secondary).