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arXiv · 2606.11168

Sasakian manifolds and spin-c Killing spinors

Alejandro Gil-García·C. S. Shahbazi
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Abstract

Using the theory of complex spinorial forms, we prove that an odd-dimensional Riemannian manifold admits a pure spin-c Killing spinor with a real Killing constant $\alpha\in\mathbb{R}^{\ast}$ if and only if it is $\alpha$-Sasakian, thereby obtaining an extension of a well-known result by A. Moroianu that, under the purity assumption, does not require simple connectivity or completeness.

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Alejandro Gil-García, C. S. Shahbazi. 2026-06-09. Sasakian manifolds and spin-c Killing spinors. https://arxiv.org/abs/2606.11168

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