Contents Online
Communications in Analysis and Geometry
Volume 23 (2015)
Number 4
Twistor geometry of Riemannian 4-manifolds by moving frames
Pages: 819 – 839
DOI: https://dx.doi.org/10.4310/CAG.2015.v23.n4.a4
Authors
Abstract
In this paper, we use the method of moving frames to characterize Riemannian 4-manifold in terms of its almost Hermitian twistor spaces $(Z, g_t, \mathbb{J}_{\pm})$. Some special metric conditions (including the balanced metric condition, the first Gauduchon metric condition) on $(Z, g_t, \mathbb{J}_{\pm})$ are studied. For the first Chern form of a natural unitary connection on the vertical tangent bundle over the twistor space $Z$, we can recover J. Fine and D. Panov’s result on the condition of the first Chern form being symplectic and P. Gauduchon’s result on the condition of the first Chern form being a $(1,1)$-form respectively.
Keywords
twistor space, anti-self-dual, principal bundle, the first Chern form
2010 Mathematics Subject Classification
Primary 53B21, 53B35, 53C28. Secondary 53C24, 53C25, 53C56.
Published 13 August 2015