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摘要翻译：
我们计算了部分标志流形F_n=SU(n+2)/S(U(n)\乘U(1)\乘U(1))的自然几乎厄米结构的Chern类和Chern数。对于所有n>1，有两个不变的复代数结构，它们是由复射影空间的全纯切丛和余切丛的射影引起的。余切丛的射影是Grassmanian的扭曲空间，它被认为是一个四元数K\\Ahler流形，由于F_n是一个3-对称空间，因此存在一个不变的近K\\Ahler结构。我们解释了不同结构与其Chern类之间的关系，并证明了F_n不是几何形式的。
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英文标题：
《Chern numbers and the geometry of partial flag manifolds》
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作者：
D. Kotschick and S. Terzic
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Differential Geometry 微分几何
分类描述：Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis
复形，接触，黎曼，伪黎曼和Finsler几何，相对论，规范理论，整体分析
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
We calculate the Chern classes and Chern numbers for the natural almost Hermitian structures of the partial flag manifolds F_n=SU(n+2)/S(U(n)\times U(1)\times U(1)). For all n>1 there are two invariant complex algebraic structures, which arise from the projectivizations of the holomorphic tangent and cotangent bundles of complex projective spaces. The projectivization of the cotangent bundle is the twistor space of a Grassmannian considered as a quaternionic K\"ahler manifold. There is also an invariant nearly K\"ahler structure, because F_n is a 3-symmetric space. We explain the relations between the different structures and their Chern classes, and we prove that F_n is not geometrically formal.
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PDF链接：
https://arxiv.org/pdf/0709.3026
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