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On local stabilities of $p$-Kähler structures

Part of: Global differential geometry Deformations of analytic structures Families, fibrations Commutative algebra: Homological methods

Published online by Cambridge University Press:  07 March 2019

Sheng Rao ,
Xueyuan Wan  and
Quanting Zhao
Sheng Rao
Affiliation:
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China email likeanyone@whu.edu.cn, raoshengmath@gmail.com
Xueyuan Wan
Affiliation:
Mathematical Sciences, Chalmers University of Technology, University of Gothenburg, 412 96 Gothenburg, Sweden email xwan@chalmers.se
Quanting Zhao
Affiliation:
School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, China email zhaoquanting@126.com, zhaoquanting@mail.ccnu.edu.cn
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Abstract

By use of a natural extension map and a power series method, we obtain a local stability theorem for $p$-Kähler structures with the $(p,p+1)$th mild $\unicode[STIX]{x2202}\overline{\unicode[STIX]{x2202}}$-lemma under small differentiable deformations.

Keywords

deformations of complex structuresdeformations and infinitesimal methodsformal methodsdeformationsHermitian and Kählerian manifolds

MSC classification

Primary: 32G05: Deformations of complex structures
Secondary: 13D10: Deformations and infinitesimal methods 14D15: Formal methods; deformations 53C55: Hermitian and Kählerian manifolds

Information

Type
Research Article
Information
Compositio Mathematica , Volume 155 , Issue 3 , March 2019 , pp. 455 - 483
Copyright
© The Authors 2019 

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Footnotes

Rao is partially supported by NSFC (Grant No. 11671305, 11771339). Zhao is partially supported by China Postdoctoral Science Foundation and NSFC (Grant No. 2016M592356 and 11801205).

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