Conformal Killing forms on nearly K\"ahler manifolds

Antonio M. Naveira; Uwe Semmelmann

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arXiv · 1903.06734

Conformal Killing forms on nearly K\"ahler manifolds

Antonio M. Naveira·Uwe Semmelmann

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Abstract

We study conformal Killing forms on compact 6-dimensional nearly K\"ahler manifolds. Our main result concerns forms of degree 3. Here we give a classification showing that all conformal Killing 3-forms are linear combinations of $d \omega$ and its Hodge dual $* d\omega$ where $\omega$ is the fundamental 2-form of the nearly K\"ahler structure. The proof is based on a fundamental integrability condition for conformal Killing forms. We have partial results in the case of conformal Killing 2-forms. In particular we show the non-existence of J-anti-invariant Killing 2-forms.

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Antonio M. Naveira, Uwe Semmelmann. 2019-03-15. Conformal Killing forms on nearly K\"ahler manifolds. https://arxiv.org/abs/1903.06734

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