Some Integration Problems in Almost-Complex and Complex Manifolds

The theory of almost-complex manifolds leads to a number of problems which properly belong to the field of differential equations. This paper deals with three such problems. The first concerns differential equations in the exterior operator d (frequently also denoted 8) on differential forms; the other two deal with holomorphic coordinates and holomorphic curves. The latter are first stated in differential-geometric terms, and then re-stated as problems in differential equations. The equivalence of these formulations is established in a separate section. The differential equations problems (Theorems I, II', III') and their proofs can be read independently. Two appendices contain underlying facts that are either not available in the form required, or can be obtained only from widely scattered sources.