A generalization of Cayley submanifolds
Abstract
Given a Kaehler manifold of complex dimension 4, we consider submanifolds of (real) dimension 4, whose Kaehler angles coincide. We call these submanifolds Cayley. We investigate some of their basic properties, and prove that (a) if the ambient manifold is a CalabiYau, the minimal Cayley submanifolds are just the Cayley submanifolds as defined by Harvey and Lawson; (b) if the ambient is a KaehlerEinstein manifold of nonzero scalar curvature, then minimal Cayley submanifolds have to be either complex or Lagrangian.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2000
 arXiv:
 arXiv:math/0002065
 Bibcode:
 2000math......2065G
 Keywords:

 Differential Geometry
 EPrint:
 15 pages, LaTeX