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On Tian–Todorov lemma and its applications to deformation of CR-structures

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Abstract

We give a new Tian–Todorov lemma on deformations of CR-structures and use it to reprove the deformation unobstructedness of normal compact strongly pseudoconvex CR-manifold under the assumption of \(d'd''\)-lemma, more faithfully following Tian–Todorov’s approach.

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Acknowledgements

This work was mainly completed during the authors’ visit to Institute of Mathematics, Academia Sinica in the summer of 2018. They would like to express their gratitude to the institute for their hospitality and the wonderful work environment during their visit, especially Professors Jih-Hsin Cheng and Chin-Yu Hsiao for many discussions on CR geometry. Last, we would like to thank Professor K. Miyajima for a useful comment on our paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, People’s Republic of China

    Sheng Rao

  2. Université de Grenoble-Alpes, Institut Fourier (Mathématiques), UMR 5582 du C.N.R.S., 100 rue des Maths, 38610, Gières, France

    Sheng Rao

  3. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, People’s Republic of China

    Yongpan Zou

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  1. Sheng Rao
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  2. Yongpan Zou
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Correspondence to Yongpan Zou.

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Sheng Rao and Yongpan Zou are partially supported by NSFC (Grant No. 11671305, 11771339, 11922115).

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Rao, S., Zou, Y. On Tian–Todorov lemma and its applications to deformation of CR-structures. Math. Z. 297, 943–960 (2021). https://doi.org/10.1007/s00209-020-02541-5

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