Killing Forms on Symmetric Spaces

Abstract

Killing forms on Riemannian manifolds are differential forms whose covariant derivative is totally skew--symmetric. We show that a compact simply connected symmetric space carries a non--parallel Killing $p$--form ($p\ge 2$) if and only if it isometric to a Riemannian product $S^k\times N$, where $S^k$ is a round sphere and $k>p$.

Cited by in corpus (7)

• Killing-Yano tensors and some applications
• Twistor Forms on Riemannian Products
• Killing forms on $2$-step nilmanifolds
• Conformally related Riemannian metrics with non-generic holonomy
• Generalized vector cross products and Killing forms on negatively curved manifolds
• Higher degree Killing forms on $2-$step nilmanifolds
• Hidden symmetries and Killing tensors on curved spaces