Hermitian manifolds with quaternion structure
نویسندگان
چکیده
منابع مشابه
Curvature of Almost Quaternion- Hermitian Manifolds
We study the decomposition of the Riemannian curvature R tensor of an almost quaternion-Hermitian manifold under the action of its structure group Sp(n)Sp(1). Using the minimal connection, we show that most components are determined by the intrinsic torsion ξ and its covariant derivative ∇̃ξ and determine relations between the decompositions of ξ ⊗ ξ, ∇̃ξ and R. We pay particular attention to the...
متن کاملSome Remarks on Quaternion-hermitian Manifolds
Nearly-quaternionic KK ahler manifolds of dimension at least 8 are shown to be quaternionic KK ahler. Restrictions on the covariant derivative of the fundamental four-form of a semi-quaternionic KK ahler are also found.
متن کاملalmost-quaternionic Hermitian manifolds
In this note we prove that if the fundamental 4-form of an almost-quaternionic Hermitian manifold (M,Q, g) of dimension 4n ≥ 8 satisfies the conformal-Killing equation, then (M,Q, g) is quaternionic-Kähler.
متن کاملSymplectic 4-manifolds with Hermitian Weyl Tensor
It is proved that any compact almost Kähler, Einstein 4-manifold whose fundamental form is a root of the Weyl tensor is necessarily Kähler.
متن کاملVanishing theorems on Hermitian manifolds
We prove the vanishing of the Dolbeault cohomology groups on Hermitian manifolds with ddc-harmonic Kähler form and positive (1, 1)-part of the Ricci form of the Bismut connection. This implies the vanishing of the Dolbeault cohomology groups on complex surfaces which admit a conformal class of Hermitian metrics, such that the Ricci tensor of the canonical Weyl structure is positive. As a coroll...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1958
ISSN: 0040-8735
DOI: 10.2748/tmj/1178244739