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On Bismut Flat Manifolds
- Source :
- Trans. Amer. Math. Soc., 373 (2020), 5747-5772
- Publication Year :
- 2016
-
Abstract
- In this paper, we give a classification of all compact Hermitian manifolds with flat Bismut connection. We show that the torsion tensor of such a manifold must be parallel, thus the universal cover of such a manifold is a Lie group equipped with a bi-invariant metric and a compatible left invariant complex structure. In particular, isosceles Hopf surfaces are the only Bismut flat compact non-K\"ahler surfaces, while central Calabi-Eckmann threefolds are the only simply-connected compact Bismut flat threefolds.<br />Comment: In this 3rd version, we add a lemma on Hermitian surfaces with flat Riemannian connection. References are updated and typos corrected
- Subjects :
- Mathematics - Differential Geometry
Subjects
Details
- Database :
- arXiv
- Journal :
- Trans. Amer. Math. Soc., 373 (2020), 5747-5772
- Publication Type :
- Report
- Accession number :
- edsarx.1603.07058
- Document Type :
- Working Paper