On minimal surfaces in a Kähler manifold of constant holomorphic sectional curvature

Author:
Jon G. Wolfson

Journal:
Trans. Amer. Math. Soc. **290** (1985), 627-646

MSC:
Primary 53C42; Secondary 58E20

DOI:
https://doi.org/10.1090/S0002-9947-1985-0792816-3

MathSciNet review:
792816

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Abstract: This paper studies minimal surfaces in Kähler manifolds of constant holomorphic sectional curvature using the technique of the moving frame. In particular, we provide a classification of the minimal two-spheres in , complex projective -space, equipped with the Fubini-Study metric. This classification can be described as follows: To each holomorphic curve in classically there is associated a particular framing of called the Frenet frame. Each element of the Frenet frame induces a minimal surface in . The classification theorem states that all minimal surfaces of topological type of the two-sphere occur in this manner. The theorem is proved using holomorphic differentials that occur naturally on minimal surfaces in Kähler manifolds of constant holomorphic sectional curvature together with the Riemann-Roch Theorem.

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DOI:
https://doi.org/10.1090/S0002-9947-1985-0792816-3

Article copyright:
© Copyright 1985
American Mathematical Society