{
  "abstract": "We classify all complex generalized spin-c Killing spinors with complex Killing function $iμ-α$ on complete Riemannian surfaces, presenting an explicit list of all possible cases. We show that, contrary to previous statements in the literature, there exist complex generalized spin-c Killing spinors on Riemannian surfaces for which $αμ\\not\\equiv0$. We illustrate the classification by providing several explicit local, compact, and complete examples, including a complete example for which $αμ>0$ everywhere. We then move to three dimensions, proving that a spin-c Riemannian three-manifold admits a complex generalized spin-c Killing spinor with complex Killing function $iμ-α$ if and only if it is a $μ$-exact trans-Sasakian manifold of type $(α,μ)$. In addition, we construct a geodesically incomplete Riemannian three-manifold equipped with a complex generalized spin-c Killing spinor for which neither $μ$ nor $α$ vanishes identically, and then prove that this is not possible if the characteristic vector field of the associated trans-Sasakian structure is complete. These results settle a conjecture by Große and Nakad (Results in Mathematics, 2015) stating that on two- and three-dimensional Riemannian manifolds the complex Killing function of any complex generalized spin-c Killing spinor must be either globally real or globally imaginary.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20568",
  "author_total": 3,
  "authors": [
    {
      "name": "José Luis Carmona Jiménez"
    },
    {
      "name": "Alejandro Gil-García"
    },
    {
      "name": "C. S. Shahbazi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d6dj8q3q9cta3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20568",
  "fulltext_url": null,
  "id": "d6dj8q3q9cta3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20568",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7222010418",
  "pdf_url": "https://arxiv.org/pdf/2610.20568",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d6dj8q3q9cta3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.20568",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20568"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Complex generalized spin-c Killing spinors in low dimensions",
  "title_text": "Complex generalized spin-c Killing spinors in low dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/d6dj8q3q9cta3",
  "venue": "arXiv",
  "versions": []
}