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… Expand

We prove that under certain conditions on the mean curvature and on the Kaehler angles, a compact submanifold M of real dimension 2n, immersed into a Kaehler-Einstein manifold N of complex dimension… Expand

We prove that under certain conditions on the mean curvature and on the Kähler angles, a compact submanifold M of real dimension 2n, immersed into a Kähler-Einstein manifold N of complex dimension… Expand

We consider F : M → N a minimal submanifold M of real dimension 2n, immersed into a Kahler-Einstein manifold N of complex dimension 2n, and scalar curvature R. We assume that n > 2 and F has equal… Expand

Assuming the ambient manifold is Kahler, the theory of complex submanifolds can be placed in the more general context of calibrated submanifolds, see [HL]. It is therefore natural to try to extend… Expand

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… Expand