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

被引：3

作者：

Barbaro, Giuseppe ^{[1
]}

机构：

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

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2021年 / 169卷

关键词：

Hermitian curvature flows; Bismut connection; Holomorphic bisectional curvature; Linear Hopf manifolds; Six-dimensional Calabi-Yau solvmanifolds; COMPLEX STRUCTURES; MANIFOLDS;

D O I：

10.1016/j.geomphys.2021.104323

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页数：17