标题： 扭曲空间上的自然埃尔米特形式的Hessian 显示英文标题

标题： Hessian of the natural Hermitian form on twistor spaces

摘要： 我们依次计算了超凯勒流形的Calabi族上的自然埃尔米特形式的海森矩阵，4维自对偶黎曼流形的扭量空间以及四元数凯勒流形的扭量空间的海森矩阵。 我们展示了超凯勒流形的Calabi族上扭量线的循环空间的强凸性性质。 我们还证明了4维非正标量曲率的自对偶爱因斯坦流形的扭量空间的1-循环空间以及四元数凯勒流形的非正标量曲率的扭量空间的1-循环空间的凸性性质。 我们验证了这样的扭量空间中不会出现非凯勒的强KT流形。 显示英文摘要

摘要： We compute the hessian of the natural Hermitian form successively on the Calabi family of a hyperk\"ahler manifold, on the twistor space of a 4-dimensional anti-self-dual Riemannian manifold and on the twistor space of a quaternionic K\"ahler manifold. We show a strong convexity property of the cycle space of twistor lines on the Calabi family of a hyperk\"ahler manifold. We also prove convexity properties of the 1-cycle space of the twistor space of a 4-dimensional anti-self-dual Einstein manifold of non-positive scalar curvature and of the 1-cycle space of the twistor space of a quaternionic K\"ahler manifold of non-positive scalar curvature. We check that no non-K\"ahler strong KT manifold occurs as such a twistor space.