A generalization of Cayley submanifolds

@article{Ghigi2000AGO,
  title={A generalization of Cayley submanifolds},
  author={Alessandro Ghigi},
  journal={International Mathematics Research Notices},
  year={2000},
  volume={2000},
  pages={787-800}
}
  • A. Ghigi
  • Published 9 February 2000
  • Mathematics
  • International Mathematics Research Notices
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… 
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We consider $F: M \to N$ a minimal oriented compact real 2n-submanifold M, immersed into a Kaehler-Einstein manifold N of complex dimension 2n, and scalar curvature R. We assume that $n \geq 2$ and F…