[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 = {Xiaodong Cao and Bo Yang},
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},
}
Xiaodong Cao; Bo Yang. A note on the almost-one-half holomorphic pinching. Comptes Rendus. Mathématique, Volume 355 (2017) no. 10, pp. 1094-1098. doi : 10.1016/j.crma.2017.09.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.09.016/
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