论文标题
Obata在七维四维触点歧管上的第一个特征值定理
The Obata first eigenvalue theorems on a seven dimensional quaternionic contact manifold
论文作者
论文摘要
我们表明，尺寸七的紧凑型四基因接触歧管满足Lichnerowicz-type较低的ricci型结合，并且具有$ p $ p $ p $ - p $ unction the Blaplacian非阴性的特征功能，只有在结构是qc-cc-cc-cc-ineinstein的结构时，才能达到其最小可能的特征。特别是，在陈述的条件下，当且仅当歧管与标准$ 3 $ -Sasakian Sphere等效时，才能达到最低特征值。
We show that a compact quaternionic contact manifold of dimension seven that satisfies a Lichnerowicz-type lower Ricci-type bound and has the $P$-function of any eigenfunction of the sub-Laplacian non-negative achieves its smallest possible eigenvalue only if the structure is qc-Einstein. In particular, under the stated conditions, the lowest eigenvalue is achieved if and only if the manifold is qc-equivalent to the standard $3$-Sasakian sphere.
