Journal of East China Normal University(Natural Science) >

2022 , Vol. 2022 >Issue 4: 26 - 30

DOI: https://doi.org/10.3969/j.issn.1000-5641.2022.04.003

Mathematics

Gradient shrinking Kähler-Ricci solitons with vanishing conditions on a Bochner tensor

  • Dong SHEN ,
  • Jiancheng LIU
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  • College of Mathematics and Statistics, Northwest Normal University, Lanzhou　730070, China

Received date: 2020-12-16

  Online published: 2022-07-19

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Abstract

In this paper, we study complete gradient shrinking K?hler-Ricci solitons with a vanishing fourth-order Bochner tensor (i.e. $\text{div}^{4}(W)=\nabla_{\bar{k}}\nabla_{j}\nabla_{\bar{i}}\nabla_{l}W_{i\bar{j}k\bar{l}}=0$ ), and obtain the corresponding classification results.

Key words： K?hler-Ricci soliton; Bochner tensor; harmonic Bochner tensor

Cite this article

Dong SHEN , Jiancheng LIU . Gradient shrinking Kähler-Ricci solitons with vanishing conditions on a Bochner tensor[J]. Journal of East China Normal University(Natural Science), 2022 , 2022(4) : 26 -30 . DOI: 10.3969/j.issn.1000-5641.2022.04.003

References

1 CAO H D. Deformation of K?hler metrics to K?hler-Einstein metrics on compact K?hler manifolds. Inventiones Mathematicae, 1985, 81, 359- 372.
2 CHEN Q, ZHU M. On rigidity of gradient K?hler-Ricci solitons with harmonic Bochner tensor. Proceedings of the American Mathematical Society, 2012, 140, 4017- 4025.
3 SU Y, ZHANG K. On the K?hler-Ricci solitons with vanishing Bochner-Weyl tensor. Acta Mathematica Scientia, 2012, 32 (3): 1239- 1244.
4 YANG F, ZHANG L D. Classification of gradient K?hler-Ricci solitons with vanishing B-tensor . Journal of Geometry and Physics, 2020, 147 (6): 393- 440.
5 CATINO G, MASTROLIA P, MONTICELLI D D. Gradient Ricci solitons with vanishing conditions on Weyl. Journal de Mathématiques Pures et Appliquées, 2017, 108, 1- 13.
6 CAO H D, ZHOU D. On complete gradient shrinking Ricci solitons. Journal of Differential Geometry, 2010, 85 (2): 175- 185.
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