论文标题
关于同构性一个Hermitian非Kähler指标
On cohomogeneity one Hermitian non-Kähler metrics
论文作者
论文摘要
我们研究了遗传歧管的几何形状，并具有与共同质量的主要轨道相同的同态构象的紧凑型谎言群体作用。特别是，我们专注于通过以下bérard-bergery构建的这些歧管的特殊类别，其中包括$ \ Mathbb C \ Mathbb c \ Mathbb p^{M-1} $，Linearear Hopf歧管和赫兹布鲁克表面上的Holomorthic Line捆绑包。我们描述了它们不变的特殊遗产指标，例如平衡，像kähler一样，多普，在当地保友，kähler，vaisman，gauduchon。此外，我们构建了一个共同体的新示例，一个遗传学指标求解了第二层神因式方程和恒定的Chern-Scalar曲率方程。
We investigate the geometry of Hermitian manifolds endowed with a compact Lie group action by holomorphic isometries with principal orbits of codimension one. In particular, we focus on a special class of these manifolds constructed by following Bérard-Bergery which includes, among the others, the holomorphic line bundles on $\mathbb C\mathbb P^{m-1}$, the linear Hopf manifolds and the Hirzebruch surfaces. We characterize their invariant special Hermitian metrics, such as balanced, Kähler-like, pluriclosed, locally conformally Kähler, Vaisman, Gauduchon. Furthermore, we construct new examples of cohomogeneity one Hermitian metrics solving the second-Chern-Einstein equation and the constant Chern-scalar curvature equation.
