Minimal Immersions of Kahler Manifolds into Euclidean Spaces |
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Authors: | di Scala Antonio J. |
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Affiliation: | The University of Hull Cottingham Road, Hull, HU6 7RX A.J.Di-Scala{at}maths.hull.ac.uk |
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Abstract: | It is proved here that a minimal isometric immersion of a Kähler-Einsteinor homogeneous Kähler-manifold into an Euclidean spacemust be totally geodesic. As an application, it is shown thatan open subset of the real hyperbolic plane RH2 cannot be minimallyimmersed into the Euclidean space. As another application, aproof is given that if an irreducible Kähler manifold isminimally immersed in a Euclidean space, then its restrictedholonomy group must be U(n), where n = dimCM. 2000 MathematicsSubject Classification 53B25 (primary); 53C42 (secondary). |
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