论文标题
在Hermitian歧管的高杜州曲率上
On the Gauduchon Curvature of Hermitian Manifolds
论文作者
论文摘要
结果表明，许多结果，以前认为是Lichnerowicz Ricci曲率的特性，对于所有Gauduchon连接的RICCI曲率都保留。我们证明存在$ t $ -Gauduchon ricci-flat指标，该指标暂停了紧凑型Sasaki-ineinstein歧管，用于所有$ t \ in（ - \ infty，1）$;特别是，对于Bismut，最低限度和荒诞的形成性连接。获得了Gauduchon Holomorthic截面曲率的单调定理，这说明了Chern连接的最大特性，并提供了有关已知现象的有关超质性和理性曲线存在的见解。此外，我们显示了冬宫度量标准的刚性结果，这些指标具有一对宽阔的圆形截面曲线，这些曲线相等，阐明了在Chen-nie最近工作中隐含的双重性。
It is shown that many results, previously believed to be properties of the Lichnerowicz Ricci curvature, hold for the Ricci curvature of all Gauduchon connections. We prove the existence of $t$--Gauduchon Ricci-flat metrics on the suspension of a compact Sasaki--Einstein manifold, for all $t \in (-\infty,1)$; in particular, for the Bismut, Minimal, and Hermitian conformal connection. A monotonicity theorem is obtained for the Gauduchon holomorphic sectional curvature, illustrating a maximality property for the Chern connection and furnishing insight into known phenomena concerning hyperbolicity and the existence of rational curves. Moreover, we show a rigidity result for Hermitian metrics which have a pair of Gauduchon holomorphic sectional curvatures that are equal, elucidating a duality implicit in the recent work of Chen--Nie.
