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53b25 (primary)

Bulletin of the London Mathematical Society (1)

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MINIMAL IMMERSIONS OF KÄHLER MANIFOLDS INTO EUCLIDEAN SPACES
Antonio J. Di Scala
Journal:

Bulletin of the London Mathematical Society / Volume 35 / Issue 6 / November 2003

Published online by Cambridge University Press:

08 October 2003, pp. 825-827

Print publication:

November 2003
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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 ${\mathbb R}H^2$ 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 $n = \dim_{\mathbb C}M$.Supported by an EPSRC Grant GR/R69174.