Holomorphic curves and metrics of negative curvature
نویسندگان
چکیده
منابع مشابه
Holomorphic Curvature of Finsler Metrics and Complex Geodesics
If D is a bounded convex domain in C , then the work of Lempert [L] and Royden-Wong [RW] (see also [A]) show that given any point p ∈ D and any non-zero tangent vector v ∈ C at p, there exists a holomorphic map φ:U → D from the unit disk U ⊂ C into D passing through p and tangent to v in p which is an isometry with respect to the hyperbolic distance of U and the Kobayashi distance of D. Further...
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The number of isolated intersections between a smooth curve in Eu-clidean space and an arbitrary hyperplane can be majorized by a weighted sum of integral Frenet curvatures of the curve. In the complex Hermitian space one can derive a similar result for holomorphic curves but with much better weights. The proof of this result is based on a generalizationof the Milnor{FF ary theorem for complex ...
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We consider the problem of extending a conformal metric of negative curvature, given outside of a neighbourhood of 0 in the unit disk D, to a conformal metric of negative curvature in D. We give conditions under which such an extension is possible, and also give obstructions to such an extension. The methods we use are based on a maximum principle and the Ahlfors–Schwarz Lemma. We also give an ...
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We prove that a smooth complex projective threefold with a Kähler metric of negative holomorphic sectional curvature has ample canonical line bundle. In dimensions greater than three, we prove that, under equal assumptions, the nef dimension of the canonical line bundle is maximal. With certain additional assumptions, ampleness is again obtained. The methods used come from both complex differen...
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ژورنال
عنوان ژورنال: Journal d'Analyse Mathématique
سال: 1976
ISSN: 0021-7670,1565-8538
DOI: 10.1007/bf02789977