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- Title
On the Curvature of the Bismut Connection: Bismut–Yamabe Problem and Calabi–Yau with Torsion Metrics.
- Authors
Barbaro, Giuseppe
- Abstract
We study two natural problems concerning the scalar and the Ricci curvatures of the Bismut connection. Firstly, we study an analog of the Yamabe problem for Hermitian manifolds related to the Bismut scalar curvature, proving that, fixed a conformal Hermitian structure on a compact complex manifold, there exists a metric with constant Bismut scalar curvature in that class when the expected constant scalar curvature is non-negative. A similar result is given in the general case of Gauduchon connections. We then study an Einstein-type condition for the Bismut Ricci curvature tensor on principal bundles over Hermitian manifolds with complex tori as fibers. Thanks to this analysis, we construct explicit examples of Calabi–Yau with torsion Hermitian structures and prove a uniqueness result for them.
- Subjects
CURVATURE; TORSION; MECHANICS (Physics); CALCULUS; HERMITIAN forms
- Publication
Journal of Geometric Analysis, 2023, Vol 33, Issue 5, p1
- ISSN
1050-6926
- Publication type
Article
- DOI
10.1007/s12220-023-01203-2