Holomorphic Embedding of Complex Curves in Spaces of Constant Holomorphic Curvature | Zendy

Issac Chavel | Zendy; H. E. Rauch | Zendy

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Holomorphic Embedding of Complex Curves in Spaces of Constant Holomorphic Curvature

Author(s) -

Issac Chavel,

H. E. Rauch

Publication year - 1972

Publication title -

proceedings of the national academy of sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 5.011

H-Index - 771

eISSN - 1091-6490

pISSN - 0027-8424

DOI - 10.1073/pnas.69.3.633

Subject(s) - holomorphic function , mathematics , pure mathematics , immersion (mathematics) , riemann surface , complex manifold , converse , embedding , moduli space , constant curvature , differential geometry , sectional curvature , manifold (fluid mechanics) , mathematical analysis , constant (computer programming) , complex projective space , scalar curvature , curvature , projective space , geometry , projective test , computer science , mechanical engineering , artificial intelligence , engineering , programming language

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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