[Une note sur le pincement holomorphe presque un demi]
Motivés par un travail précédent de Zheng et du second auteur, nous étudions les constantes de pincement des variétés kählériennes compactes avec courbure sectionnelle holomorphe positive. En particulier, nous prouvons un théorème de l'écart sur des variétés kählériennes de courbure sectionnelle holomorphe avec pincement presque un demi. La preuve s'appuie sur le travail de Petersen et de Tao sur les variétés riemanniennes avec une courbure sectionnelle presque -pincée.
Motivated by a previous work by Zheng and the second-named author, we study pinching constants of compact Kähler manifolds with positive holomorphic sectional curvature. In particular, we prove a gap theorem on Kähler manifolds with almost-one-half pinched holomophic sectional curvature. The proof is motivated by the work of Petersen and Tao on Riemannian manifolds with almost-quarter-pinched sectional curvature.
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@article{CRMATH_2017__355_10_1094_0,
author = {Cao, Xiaodong and Yang, Bo},
title = {A note on the almost-one-half holomorphic pinching},
journal = {Comptes Rendus. Math\'ematique},
pages = {1094--1098},
publisher = {Elsevier},
volume = {355},
number = {10},
year = {2017},
doi = {10.1016/j.crma.2017.09.016},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2017.09.016/}
}
TY - JOUR AU - Cao, Xiaodong AU - Yang, Bo TI - A note on the almost-one-half holomorphic pinching JO - Comptes Rendus. Mathématique PY - 2017 SP - 1094 EP - 1098 VL - 355 IS - 10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2017.09.016/ DO - 10.1016/j.crma.2017.09.016 LA - en ID - CRMATH_2017__355_10_1094_0 ER -
%0 Journal Article %A Cao, Xiaodong %A Yang, Bo %T A note on the almost-one-half holomorphic pinching %J Comptes Rendus. Mathématique %D 2017 %P 1094-1098 %V 355 %N 10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2017.09.016/ %R 10.1016/j.crma.2017.09.016 %G en %F CRMATH_2017__355_10_1094_0
Cao, Xiaodong; Yang, Bo. A note on the almost-one-half holomorphic pinching. Comptes Rendus. Mathématique, Tome 355 (2017) no. 10, pp. 1094-1098. doi : 10.1016/j.crma.2017.09.016. http://www.numdam.org/articles/10.1016/j.crma.2017.09.016/
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