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arXiv · 2103.12405

Quaternionic $k$-vector fields on quaternionic K\"{a}hler manifolds

Takayuki Moriyama·Takashi Nitta
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Abstract

In this paper, we define a differential operator as a modified Dirac operator. Using the operator, we introduce a quaternionic $k$-vector field on a quaternionic K\"{a}hler manifold and show that any quaternionic $k$-vector field corresponds to a holomorphic $k$-vector field on the twistor space. We calculate the dimension of the space of quaternionic $k$-vector fields on $\mathbb{H}P^n$.

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Takayuki Moriyama, Takashi Nitta. 2021-03-23. Quaternionic $k$-vector fields on quaternionic K\"{a}hler manifolds. https://arxiv.org/abs/2103.12405

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