标题： 带有高阶势的Killing旋量方程 显示英文标题

标题： The Killing spinor equation with higher order potentials

摘要： 设 (M^n,g) 为一个黎曼旋流形。 IIa 型弦理论中带有四形式通量的超引力模型的基本方程涉及一个三形式 T，一个四形式 F，一个依赖于\nabla ^g，T，F 的旋矢协变导数\nabla ，以及一个\nabla -平行旋矢场\Psi 。 我们通过不可积特殊几何的方法对这一旋矢场方程组进行分类并构造了许多显式族解。 后者包括维数 5 和 7 的\alpha -Sasakian 结构，维数 6 的几乎凯勒结构以及维数 7 的共校化 G_2-结构。 我们证明还有几个例子也满足能量-动量张量的附加约束条件。 显示英文摘要

摘要： Let (M^n,g) be a Riemannian spin manifold. The basic equations in supergravity models of type IIa string theory with 4-form flux involve a 3-form T, a 4-form F, a spinorial covariant derivative \nabla depending on \nabla^g, T, F, and a \nabla-parallel spinor field \Psi. We classify and construct many explicit families of solutions to this system of spinorial field equations by means of non-integrable special geometries. The latter include \alpha-Sasakian structures in dimensions 5 and 7, almost Hermitian structures in dimension 6 and cocalibrated G_2-structures in dimension 7. We show that there are several examples also satisfying an additional constraint for the energy-momentum tensor.