论文标题
第二类曲率操作员的自动限制
Holonomy restrictions from the curvature operator of the second kind
论文作者
论文摘要
我们表明，第二种$ n $ nonemanngative或$ n $ n $ nonemanngative或$ n $ n $ n $ n $ nonnonpastor的曲率运算符具有限制的自动固体$ so（n）$或平整。结果不取决于完整性，并且可以改善空间是爱因斯坦或Kähler。特别是，如果本地对称空间具有$ n $ nonnengative或$ n $ nononpoldasity curvature otervature the Secends的曲率运算符，则它具有恒定的曲率。当局部对称的空间不可理理时，可以将其提高到$ \ frac {3n} {2} {2} \ frac {n+2} {n+4} $ - nonnonegative或$ \ frac {3n} {3n} {2} {2} \ frac {n+2} {n+2} {n+4} {n+4} $ non} $ non} $ nonposive sytertation sestication sytertation。
We show that an $n$-dimensional Riemannian manifold with $n$-nonnegative or $n$-nonpositive curvature operator of the second kind has restricted holonomy $SO(n)$ or is flat. The result does not depend on completeness and can be improved provided the space is Einstein or Kähler. In particular, if a locally symmetric space has $n$-nonnegative or $n$-nonpositive curvature operator of the second kind, then it has constant curvature. When the locally symmetric space is irreducible this can be improved to $\frac{3n}{2}\frac{n+2}{n+4}$-nonnegative or $\frac{3n}{2}\frac{n+2}{n+4}$-nonpositive curvature operator of the second kind.
