Given a Kähler manifold of complex dimension 4, we consider submanifolds of (real) dimension 4 whose Kähler angles coincide. We call these submanifolds Cayley. We investigate some of their basic properties, and prove that: (a) if the ambient manifold is Calabi-Yau, the minimal Cayley submanifolds are exactly the Cayley submanifolds as defined by Harvey and Lawson [HL1]; (b) if the ambient is a Kähler-Einstein manifold of nonzero scalar curvature, then minimal Cayley submanifolds have to be either complex or Lagrangian
Ghigi, A. (2000). A generalization of Cayley submanifolds. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2000(15), 787-800 [10.1155/S107379280000043X].
A generalization of Cayley submanifolds
GHIGI, ALESSANDRO CALLISTO
2000
Abstract
Given a Kähler manifold of complex dimension 4, we consider submanifolds of (real) dimension 4 whose Kähler angles coincide. We call these submanifolds Cayley. We investigate some of their basic properties, and prove that: (a) if the ambient manifold is Calabi-Yau, the minimal Cayley submanifolds are exactly the Cayley submanifolds as defined by Harvey and Lawson [HL1]; (b) if the ambient is a Kähler-Einstein manifold of nonzero scalar curvature, then minimal Cayley submanifolds have to be either complex or Lagrangian
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