Holomorphic Embedding of Complex Curves in Spaces of Constant Holomorphic Curvature

  1. Issac Chavel1 and
  2. Harry E. Rauch*
  1. 1The City College of The City University of New York, 33 West 42nd St., New York, N.Y. 10036
  2. *The Graduate Center of The City University of New York, 33 West 42nd St., New York, N.Y. 10036

Abstract

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.

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  1. PNAS March 1, 1972 vol. 69 no. 3 633-635
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