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Conference on Complex Analysis and Mathematical Physics, dedicated to the 70th birthday of A. G. Sergeev
March 21, 2019 11:20–12:00, Moscow, Steklov Mathematical Institute, Gubkina St., 8
 


Rigidity of compact holomorphic curves in compact complex parallelizable manifolds ΓSL(2,C) and its geometric applications

Ryoichi Kobayashi
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Ryoichi Kobayashi
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Abstract: Let ΓSL(2,C) be a cocompact lattice and X=ΓSL(2,C) the associated compact complex parallelizable manifold. We show that any non-constant holomorphic map f:MX from a compact Riemann surface M into X decomposes as f=thα, where α:MAlb(M) is the Albanese map, h:Alb(M)X=ΓSL(2,C) has its image in a maximal torus T=ΓAAZC in X (A being a maximal torus in SL(2,C)) defining an algebraic group homomorphism h:Alb(M)T=(AΓ)A, and finally t is a right translation by some element of SL(2,C). The proof is based on Bishop's measure theoretic criterion of analyticity of sets combined with a simple observation in hyperbolic geometry.
I will discuss some applications of this rigidity.

Language: English
 
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