Vol. 110, No. 1, 1984

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On the holomorphy of maps from a complex to a real manifold

Subhashis Nag

Vol. 110 (1984), No. 1, 191–201

Let f : X Y be a C1-submersion from a complex manifold X to a real C1-manifold Y . One main object of this paper is to prove two sets of necessary and sufficient conditions which will guarantee that Y can be equipped with a complex structure making f holomorphic. We provide a generic counterexample to show the essential nature of the conditions we establish.

The second set of conditions (Theorem 3) apply even when X is a complex Banach manifold. This theorem is then used to prove the existence of the natural complex structure on the Teichmuller spaces of Riemann surfaces of finite type.

Mathematical Subject Classification 2000
Primary: 32G05
Secondary: 32G15, 32H99
Received: 16 February 1982
Published: 1 January 1984
Subhashis Nag