A Coincidence Theorem for Holomorphic Maps to $G/P$
Canadian mathematical bulletin, Tome 46 (2003) no. 2, pp. 291-298
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The purpose of this note is to extend to an arbitrary generalized Hopf and Calabi-Eckmann manifold the following result of Kalyan Mukherjea: Let ${{V}_{n}}={{\mathbb{S}}^{2n+1}}\times {{\mathbb{S}}^{2n+1}}$ denote a Calabi-Eckmann manifold. If $f,g:\,{{V}_{n}}\to {{\mathbb{P}}^{n}}$ are any two holomorphic maps, at least one of them being non-constant, then there exists a coincidence: $f(x)\,=\,g(x)$ for some $x\in {{V}_{n}}$ . Our proof involves a coincidence theorem for holomorphic maps to complex projective varieties of the form $G/P$ where $G$ is complex simple algebraic group and $P\,\subset \,G$ is a maximal parabolic subgroup, where one of the maps is dominant.
Sankaran, Parameswaran. A Coincidence Theorem for Holomorphic Maps to $G/P$. Canadian mathematical bulletin, Tome 46 (2003) no. 2, pp. 291-298. doi: 10.4153/CMB-2003-029-4
@article{10_4153_CMB_2003_029_4,
author = {Sankaran, Parameswaran},
title = {A {Coincidence} {Theorem} for {Holomorphic} {Maps} to $G/P$},
journal = {Canadian mathematical bulletin},
pages = {291--298},
year = {2003},
volume = {46},
number = {2},
doi = {10.4153/CMB-2003-029-4},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-029-4/}
}
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