A Hermitian Curvature Flow

Jixiang Fu , Jieming Yang

Chinese Annals of Mathematics, Series B ›› 2022, Vol. 43 ›› Issue (5) : 845 -854.

PDF
Chinese Annals of Mathematics, Series B ›› 2022, Vol. 43 ›› Issue (5) : 845 -854. DOI: 10.1007/s11401-022-0362-1
Article

A Hermitian Curvature Flow

Author information +
History +
PDF

Abstract

A Hermitian curvature flow on a compact Calabi-Yau manifold is proposed and a regularity result is obtained. The solution of the flow, if exists, is a balanced Hermitian-Einstein metric.

Keywords

Hermitian Yang-Mills / Evolution equations / Regularity

Cite this article

Download citation ▾
Jixiang Fu, Jieming Yang. A Hermitian Curvature Flow. Chinese Annals of Mathematics, Series B, 2022, 43(5): 845-854 DOI:10.1007/s11401-022-0362-1

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

Friedman R. On threefolds with trivial canonical bundle. Proc. Sympos. Pure Math., 1989, 53: 103-134

[2]

Friedman R. The $\partial \overline \partial $-lemma for general Clemens manifolds. Pure Appl. Math. Q., 2019, 15: 1001-1028

[3]

Fu J X. On non-Kähler Calabi-Yau threefolds with balanced metrics, 2010, New Delhi: Hindustan Book Agency 705-716 Volume II

[4]

Fu J X, Li J, Yau S-T. Balanced metrics on non-Kähler Calabi-Yau threefolds. J. Differential Geom., 2012, 90: 81-130

[5]

Gill M. Convergence of the parabolic complex Monge-Ampère equation on compact Hermitian manifolds. Comm. Anal. Geom., 2011, 19(2): 277-303

[6]

Hamilton R. A compactness property for solutions of the Ricci flow. Amer. J. Math., 1995, 117: 545-572

[7]

Klemyatin, N., Convergence for Hermitian manifolds and the Type IIB flow, 2021, arXiv: 2109.00312.

[8]

Lu, P. and Tian, G., Complex structures on connected sums of S 3 × S 3, Manifolds and geometry, Pisa, 1993, 284–293.

[9]

Phong D H, Picard S, Zhang X. Geometric flows and Strominger systems. Math. Z., 2018, 288: 101-113

[10]

Phong D H, Picard S, Zhang X. Anomaly flows. Comm. Anal. Geom., 2018, 26(4): 955-1008

[11]

Phong D H, Picard S, Zhang X. A flow of conformally balanced metrics with Kähler fixed points. Math. Ann., 2019, 374: 2005-2040

[12]

Sherman M, Weinkove B. Local Calabi and curvature estimates for the Chern-Ricci flow. New York J. Math., 2013, 19: 565-582

[13]

Streets J, Tian G. A parabolic flow of pluriclosed metrics. Int. Math. Res. Not., 2010, 2010(16): 3101-3133

[14]

Streets J, Tian G. Hermitian curvature flow. J. Eur. Math. Soc., 2011, 13: 601-634

[15]

Streets J, Tian G. Regularity results for pluriclosed flow. Geom. Top., 2013, 17: 2389-2429

[16]

Tosatti V. Non-Kähler Calabi-Yau maniolds. Contemp. Math., 2015, 644: 261-277

[17]

Tosatti V, Weinkove B. On the evolution of a Hermitian metric by its Chern-Ricci form. J. Differential Geom., 2015, 99: 125-163

AI Summary AI Mindmap
PDF

105

Accesses

0

Citation

Detail

Sections
Recommended

AI思维导图

/