A Coincidence Theorem for Holomorphic Maps to $G/P$

[摘要] The purpose of this note is to extend to an arbitrary generalized Hopfand Calabi-Eckmann manifold the following result of Kalyan Mukherjea:Let $V_n = mathbb{S}^{2n+1} imes mathbb{S}^{2n+1}$ denote aCalabi-Eckmann manifold. If $f,g colon V_n longrightarrowmathbb{P}^n$ are any two holomorphic maps, at least one of them beingnon-constant, then there exists a coincidence: $f(x)=g(x)$ for some$xin V_n$. Our proof involves a coincidence theorem for holomorphicmaps to complex projective varieties of the form $G/P$ where $G$ iscomplex simple algebraic group and $Psubset G$ is a maximal parabolicsubgroup, where one of the maps is dominant.

[学科分类] 数学（综合）

[关键词] group cohomology;$L^p$-cohomology;central element of infinite order;harmonic function;continuous linear functional