Geodesic
A Coincidence Theorem for Holomorphic Maps to $G/P$
Canadian mathematical bulletin, Tome 46 (2003) no. 2, pp. 291-298

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2003-029-4
Mots-clés : 32H02, 54M20 
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
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