A generalization of Cayley submanifolds

Details A generalization of Cayley submanifolds A generalization of Cayley submanifolds

2000-02-09

arxiv.org/abs/math/0002065v1

Mathematics

Differential Geometry

15 pages, LaTeX

Scientific paper

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 Calabi-Yau, the minimal Cayley submanifolds are just the Cayley submanifolds as defined by Harvey and Lawson; (b) if the ambient is a Kaehler-Einstein manifold of non-zero scalar curvature, then minimal Cayley submanifolds have to be either complex or Lagrangian.

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