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Mathematics > Differential Geometry

arXiv:1812.09633 (math)
[Submitted on 23 Dec 2018 (v1), last revised 10 May 2021 (this version, v3)]

Title:Canonical almost complex structures on ACH Einstein manifolds

Authors:Yoshihiko Matsumoto
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Abstract:On asymptotically complex hyperbolic (ACH) Einstein manifolds, we consider a certain variational problem for almost complex structures compatible with the metric, for which the linearized Euler-Lagrange equation at Kähler-Einstein structures is given by the Dolbeault Laplacian acting on $(0,1)$-forms with values in the holomorphic tangent bundle. A deformation result of Einstein ACH metrics associated with critical almost complex structures for this variational problem is given. It is also shown that the asymptotic expansion of a critical almost complex structure is determined by the induced (possibly non-integrable) CR structure on the boundary at infinity up to a certain order.
Comments: 28 pages. The statement of Theorem 1.2 is modified; substantial corrections and clarifications are added throughout the text
Subjects: Differential Geometry (math.DG); Complex Variables (math.CV)
MSC classes: 53C15 (Primary) 32T15, 32V15, 53B35, 53C25 (Secondary)
Cite as: arXiv:1812.09633 [math.DG]
  (or arXiv:1812.09633v3 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.1812.09633
Journal reference: Pacific J. Math. 314 (2021) 375-410
Related DOI: https://doi.org/10.2140/pjm.2021.314.375

Submission history

From: Yoshihiko Matsumoto [view email]
[v1] Sun, 23 Dec 2018 01:48:51 UTC (33 KB)
[v2] Tue, 25 Jun 2019 23:47:57 UTC (33 KB)
[v3] Mon, 10 May 2021 10:55:42 UTC (35 KB)
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