✦ LIBER ✦
Harmonic and holomorphic 1-forms on compact balanced Hermitian manifolds
✍ Scribed by Georgi Ganchev; Stefan Ivanov
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 97 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0926-2245
No coin nor oath required. For personal study only.
✦ Synopsis
On compact balanced Hermitian manifolds we obtain obstructions to the existence of harmonic 1-forms, ∂-harmonic (1, 0)-forms and holomorphic (1, 0)-forms in terms of the Ricci tensors with respect to the Riemannian curvature and the Hermitian curvature. Necessary and sufficient conditions the (1, 0)-part of a harmonic 1-form to be holomorphic and vice versa, a real 1-form with a holomorphic (1, 0)-part to be harmonic are found. The vanishing of the first Dolbeault cohomology groups of the twistor space of a compact irreducible hyper-Kähler manifold is shown.