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Minimal Immersions of Kähler Manifolds into Euclidean Spaces
Author(s) -
di Scala Antonio J.
Publication year - 2003
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609303002492
Subject(s) - mathematics , holonomy , pure mathematics , hyperbolic space , manifold (fluid mechanics) , immersion (mathematics) , euclidean space , geodesic , seven dimensional space , euclidean geometry , euclidean group , mathematics subject classification , mathematical analysis , euclidean distance matrix , affine space , geometry , mechanical engineering , engineering , affine transformation
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 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 C M . 2000 Mathematics Subject Classification 53B25 (primary); 53C42 (secondary).