论文标题
Hermitian流形的曲率的新阳性条件
A new positivity condition for the curvature of Hermitian manifolds
论文作者
论文摘要
在本说明中，我们为Hermitian歧管的曲率引入了一种新型的阳性条件，该曲率概括了非二次正交双式曲率的概念，以对非kähler案例。我们为封闭的$（1，1）$ - 形式得出了一种自然而然的状态的bochner公式，并证明，如果赫米尔人的多种流形满足了我们的积极状态，那么任何类$α\ in H^{1，1，1} _ {bc} _ {bc}（x）$都可以由封闭的$（1，1，1，1，1）$ - 形式来代表。最后，我们表明，这种弯曲的阳性条件在某些广义的Hopf流形和某些Vaisman流形上存在。
In this note, we introduce a new type of positivity condition for the curvature of a Hermitian manifold, which generalizes the notion of nonnegative quadratic orthogonal bisectional curvature to the non-Kähler case. We derive a Bochner formula for closed $(1, 1)$-forms from which this condition appears naturally and prove that if a Hermitian manifold satisfy our positivity condition, then any class $α\in H^{1, 1}_{BC}(X)$ can be represented by a closed $(1, 1)$-form which is parallel with respect to the Bismut connection. Lastly, we show that such a curvature positivity condition holds on certain generalized Hopf manifolds and on certain Vaisman manifolds.
