论文标题
QuaternionicKähler歧管的曲率与$ s^1 $ -smmetry
Curvature of quaternionic Kähler manifolds with $S^1$-symmetry
论文作者
论文摘要
我们研究了HK/QK对应关系下的连接和曲率的行为，证明了表达Levi-Civita连接的简单公式和QuaternionicKähler侧面的Riemann曲率张量，就初始的Hyper-Kähhler数据而言。由于Alekseevsky，我们的曲率公式完善了众所周知的分解定理。作为一种应用，我们计算了一系列完全QuaternionicKähler歧管的曲率张量的规范，这些歧管由平坦的Hyper-Kähler歧管产生。我们以此来推断这些流形是同一性的。
We study the behavior of connections and curvature under the HK/QK correspondence, proving simple formulae expressing the Levi-Civita connection and Riemann curvature tensor on the quaternionic Kähler side in terms of the initial hyper-Kähler data. Our curvature formula refines a well-known decomposition theorem due to Alekseevsky. As an application, we compute the norm of the curvature tensor for a series of complete quaternionic Kähler manifolds arising from flat hyper-Kähler manifolds. We use this to deduce that these manifolds are of cohomogeneity one.
