Holomorphic embedding of complex curves in spaces of constant holomorphic curvature.
A special case of Wirtinger's theorem asserts that a complex curve (two-dimensional) holomorphically embedded in a Kaehler manifold is a minimal surface. The converse is not necessarily true. Guided by considerations from the theory of moduli of Riemann surfaces, we discover (among other results) sufficient topological and differential-geometric conditions for a minimal (Riemannian) immersion of a 2-manifold in complex projective space with the Fubini-Study metric to be holomorphic.
The City College of The City University of New York, 33 West 42nd St., New York, N.Y. 10036.
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