2013
DOI: 10.4310/mrl.2013.v20.n1.a3
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On the fundamental groups of compact Sasakian manifolds

Xiaoyang Chen

Abstract: Abstract. We study the fundamental groups of compact Sasakian manifolds, which we call Sasaki groups. It is shown that the fundamental group of any compact Hodge manifold is Sasaki. In particular, all finite groups are Sasaki. On the other hand, we show that there exist many restrictions on Sasaki groups. We also study the Abel-Jacobi map of a compact Sasakian manifold and its applications to Sasaki groups.

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Cited by 14 publications
(22 citation statements)
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“…There are some well-known topological obstructions to the existence of a Sasakian structure on a compact K-contact manifold (refer to, e.g. [6,2,4,9,1]). …”
Section: Introduction and Main Resultsmentioning
confidence: 99%
“…There are some well-known topological obstructions to the existence of a Sasakian structure on a compact K-contact manifold (refer to, e.g. [6,2,4,9,1]). …”
Section: Introduction and Main Resultsmentioning
confidence: 99%
“…Our second main purpose in this article is to generalize the concepts of Kähler hyperbolicity and non-ellipticity by terming a condition by "Kähler exactness", which has been used in [CY17], and show that a Kähler exact manifold of general type has ample canonical bundle. Recall that on a compact Kähler manifold any Kähler form is closed but can never be exact, which motivates us to introduce the following notion.…”
Section: Furthermorementioning
confidence: 99%
“…Recently B.-L. Chen and X. Yang made some important progress towards this question and the Hopf Conjecture 1.1 in two articles [CY18] and [CY17]. In the first one [CY18], They showed that a compact Kähler manifold homotopy equivalent to a negatively curved compact Riemannian manifold admits a Kähler-Einstein metric of negative Ricci curvature ([CY18, Thm 1.1]).…”
Section: Introductionmentioning
confidence: 99%
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