The Dimension Function of Holomorphic Spaces of a Real Submanifold of an Almost Complex Manifold
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Let M be a real submanifold of an almost complex manifold \((\overline M ,\overline J )\) and let \(H_x = T_x M \cap \overline J (T_x M)\) be the maximal holomorphic subspace, for each x∈ M. We prove that c:M→ℕ,c(x)=dimℝHx is upper-semicontinuous.
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