论文标题
Quaternion-kähler对称空间的一体性
Integrability of quaternion-Kähler symmetric spaces
论文作者
论文摘要
我们发现，Quaternionic自动形态在$ \ Mathfrak {g} $的表示方面，通过Quaternionic Automorthisms在Quaternionic Automorthism上存在谎言组$ G $的动作的必要条件。我们检查了这种情况，并证明$ n \ geq 2 $的riemannian对称空间$ 4N $具有不变的整合性几乎是quaternionic结构，并且仅当它是Quaternionic载体矢量空间，Quaternionic hypbolic空间或Quaternionic Projectiv的投射空间。
We find a necessary condition for the existence of an action of a Lie group $G$ by quaternionic automorphisms on an integrable quaternionic manifold in terms of representations of $\mathfrak{g}$. We check this condition and prove that a Riemannian symmetric space of dimension $4n$ for $n\geq 2$ has an invariant integrable almost quaternionic structure if and only if it is quaternionic vector space, quaternionic hyperbolic space or quaternionic projective space.
