Griffiths positivity for Bismut curvature and its behaviour along Hermitian curvature flows
نویسندگان
چکیده
In this note we study a positivity notion for the curvature of Bismut connection; more precisely, Bismut-Griffiths-positivity complex Hermitian non-Kähler manifolds. Since Kähler-Ricci flow preserves and regularizes usual Griffiths investigate behaviour under action flows. particular two concrete classes examples, namely, linear Hopf manifolds six-dimensional Calabi-Yau solvmanifolds with holomorphically-trivial canonical bundle. From these examples identify some flows which do not preserve Bismut-Griffiths-non-negativity.
منابع مشابه
Hermitian Curvature Flow
We define a functional for Hermitian metrics using the curvature of the Chern connection. The Euler-Lagrange equation for this functional is an elliptic equation for Hermitian metrics. Solutions to this equation are related to Kähler-Einstein metrics, and are automatically Kähler-Einstein under certain conditions. Given this, a natural parabolic flow equation arises. We prove short time existen...
متن کاملCurvature in Hermitian Metric
Hermitian metric has the peculiarity of favoring negative curvature over positive curvature. We shall explain this phenomenon by pointing out that in the case of an isometric analytic imbedding the relative curvature is on the whole negative; also, by reduction to a limiting case of imbedding we shall explain why an invariant metric in the theory of Fuchsian groups is likely to be hyperbolic; s...
متن کاملA Condition for Positivity of Curvature
Introduction The question of positivity of curvature on bundles arose in the middle 60's with O'Neills theorem [O], according to which riemannian submersions increase the sectional curvature. In the early 70's Cheeger and Gromoll in their notable paper [C-G], showed that if an open manifold has a complete riemannian metric with non-negative sectional curvature then it is the total space of a ve...
متن کاملNonlocal Curvature Flows
This paper aims at building a unified framework to deal with a wide class of local and nonlocal translation-invariant geometric flows. We introduce a class of nonlocal generalized mean curvatures and prove the existence and uniqueness for the level set formulation of the corresponding geometric flows. We then introduce a class of generalized perimeters, whose first variation is an admissible ge...
متن کاملImage Processing: Flows under Min/Max Curvature and Mean Curvature
part, based on a local decision. This approach has several We present a class of PDE-based algorithms suitable for key virtues. First, it contains only one enhancement paramimage denoising and enhancement. The techniques are applicaeter, which in most cases is automatically chosen. Second, ble to both salt-and-pepper gray-scale noise and full-image the scheme automatically picks the stopping cr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2021
ISSN: ['1879-1662', '0393-0440']
DOI: https://doi.org/10.1016/j.geomphys.2021.104323