论文标题
在简单连接的5个manifolds上存在带有积极生物曲率曲率的Riemannian指标
Existence of Riemannian metrics with positive biorthogonal curvature on simply connected 5-manifolds
论文作者
论文摘要
使用贝蒂奥的最新工作，我们表明Wilking对$ S^2 \ times s^3 $在$ S^2 \ times s^3 $上的一阶整形曲线变形产生了一个由2个平面的截面曲率平均值的截面平均值的家庭，这些指标由2个平面的任何一对曲线分离，这些曲率由2-大距离在2-少数距离中的微小距离分离。 Smale的结果使我们能够得出结论，每个封闭式将5个manifold与无扭转的同源性和琐碎的第二个Stiefel-Whitney类连接在一起，承认了一个riemannian指标，并具有严格的任何一对正交2-计划的分节曲线的正平均值。
Using recent work of Bettiol, we show that a first-order conformal deformation of Wilking's metric of almost-positive sectional curvature on $S^2\times S^3$ yields a family of metrics with strictly positive average of sectional curvatures of any pair of 2-planes that are separated by a minimal distance in the 2-Grassmanian. A result of Smale's allows us to conclude that every closed simply connected 5-manifold with torsion-free homology and trivial second Stiefel-Whitney class admits a Riemannian metric with a strictly positive average of sectional curvatures of any pair of orthogonal 2-planes.
