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In this note we define the measure of holomorphicness μ(M) of a compact real submanifold M of an almost Hermitian manifold (M,J,g). The number p(M) ∈ [0,1] verifies the following properties: M is a complex submanifold iff μ(M) = 1; if dim M is odd, then p(M) = 0. Explicit examples of surfaces in C 2 are obtained, showing that μ(S 2 ) = 1/5 and that 0 < μ(T) ≤ 3/8, T being the Clifford torus.

The measure of holomorphicness of a real submanifold of an almost Hermitian manifold