Griffiths positivity for Bismut curvature and its behaviour along Hermitian curvature flows

JOURNAL OF GEOMETRY AND PHYSICS

卷:169

Article

Barbaro, Giuseppe¹ 

[1] Univ Sapienza, Dipartimento Matemat Guido Castelnuovo, Piazzale Aldo Moro 5, I-00185 Rome, Italy

关键词: Hermitian curvature flows;    Bismut connection;    Holomorphic bisectional curvature;    Linear Hopf manifolds;    Six-dimensional Calabi-Yau solvmanifolds;   

DOI  :  10.1016/j.geomphys.2021.104323

来源: Elsevier

【 摘 要 】

In this note we study a positivity notion for the curvature of the Bismut connection; more precisely, we study the notion of Bismut-Griffiths-positivity for complex Hermitian non-Kahler manifolds. Since the Kahler-Ricci flow preserves and regularizes the usual Griffiths positivity we investigate the behaviour of the Bismut-Griffiths-positivity under the action of the Hermitian curvature flows. In particular we study two concrete classes of examples, namely, linear Hopf manifolds and six-dimensional Calabi-Yau solvmanifolds with holomorphically-trivial canonical bundle. From these examples we identify some Hermitian curvature flows which do not preserve Bismut-Griffiths-non-negativity. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

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