Kenmotsu流形与spin-c Killing旋量
Kenmotsu manifolds and spin-c Killing spinors
AI总结：
该研究拓展了第一作者的结果，证明奇数维黎曼流形存在特定spin-c Killing旋量等价于其为精确$\mu$-Kenmotsu流形，还通过两种理论结合给出刻画证明并描述了该流形的整体结构。
AI中文摘要：
利用复旋量形式理论，我们证明：奇数维黎曼流形若存在带有虚Killing函数$i\mu$的纯spin-c Killing旋量，当且仅当它是一个精确$\mu$-Kenmotsu流形，从而拓展了第一作者近期的一项结果——在纯性假设下，该结果无需简单连通性或完备性条件。随后，我们用带向量挠率的度量联络重新解释$\mu$-Kenmotsu流形，并结合复旋量形式理论与带挠率的度量联络理论，给出该刻画的第二个证明。最后，我们通过Morse-Bott理论描述精确$\mu$-Kenmotsu流形的整体结构。
英文摘要：
Using the theory of complex spinorial forms, we prove that an odd-dimensional Riemannian manifold admits a pure spin-c Killing spinor with an imaginary Killing function $iμ$ if and only if it is an exact $μ$-Kenmotsu manifold, thereby obtaining an extension of a recent result by the first named author that, under the purity assumption, does not require simple connectivity or completeness. We then reinterpret $μ$-Kenmotsu manifolds in terms of metric connections with vectorial torsion and give a second proof of this characterization, combining the theory of complex spinorial forms with the theory of metric connections with torsion. Finally, we describe the global structure of exact $μ$-Kenmotsu manifolds by means of Morse-Bott theory.
