We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
On Compact Hermitian Manifolds with Flat Gauduchon Connections.
- Authors
Yang, Bo; Zheng, Fang Yang
- Abstract
Given a Hermitian manifold (Mn, g), the Gauduchon connections are the one parameter family of Hermitian connections joining the Chern connection and the Bismut connection. We will call ∇s=(1−s2)∇c+s2∇b<inline-graphic></inline-graphic> the s-Gauduchon connection of M, where ∇c and ∇b are respectively the Chern and Bismut connections. It is natural to ask when a compact Hermitian manifold could admit a flat s-Gauduchon connection. This is related to a question asked by Yau. The cases with s = 0 (a flat Chern connection) or s = 2 (a flat Bismut connection) are classified respectively by Boothby in the 1950s or by the authors in a recent joint work with Q. Wang. In this article, we observe that if either s≥4+23≈7.46<inline-graphic></inline-graphic> or s≤4−23≈0.54<inline-graphic></inline-graphic> and s ≠ 0, then g is Kähler. We also show that, when n = 2, g is always Kähler unless s = 2. Therefore non-Kähler compact Gauduchon flat surfaces are exactly isosceles Hopf surfaces.
- Subjects
HERMITIAN structures; COMPLEX manifolds; GEOMETRIC connections; H-spaces; KAHLERIAN manifolds; MANIFOLDS (Mathematics)
- Publication
Acta Mathematica Sinica, 2018, Vol 34, Issue 8, p1259
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-018-7409-y