{
  "abstract": "Let $(M,ω,\\mathcal{F}_1,\\mathcal{F}_2)$ be a bi-Lagrangian manifold. For a distribution $\\mathcal{D}\\subseteq TM$, we characterize when the subbundle $N^{*t}\\mathcal{D}:=\\mathcal{D}\\oplus N^*\\mathcal{D}$ of the Whitney sum $W=TM\\oplus T^*M$ is a Dirac structure for both the untwisted and $(H,θ)$-twisted Courant brackets. Consequently, every bi-Lagrangian structure canonically determines a pair of transverse Dirac structures. the associated bi-Lagrangian connection, also called the Hess connection $\\nabla$ induces a linear connection on $W$ with respect to which both Dirac subbundles are parallel, thereby establishing a natural link between bi-Lagrangian geometry and Courant Dirac geometry. We also construct induced bi-Lagrangian structures on $TM$, $T^*M$, and $W$, and study the relation between their affineness and that of the original structure. We also lift to these bundles the canonical action of the symplectomorphism group on bi-Lagrangian structures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.11804",
  "author_total": 3,
  "authors": [
    {
      "name": "Bertuel Tangue Ndawa"
    },
    {
      "name": "Ferdinand Ngakeu"
    },
    {
      "name": "Nasser Saipele Nansidi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dakj8937prp9c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.11804",
  "fulltext_url": null,
  "id": "dakj8937prp9c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.11804",
  "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.DS"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7168300545",
  "pdf_url": "https://arxiv.org/pdf/2607.11804",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dakj8937prp9c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2607.11804",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.11804"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Bi-Lagrangian and transverse Dirac structures induced on the Whitney sum",
  "title_text": "Bi-Lagrangian and transverse Dirac structures induced on the Whitney sum",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/dakj8937prp9c",
  "venue": "arXiv",
  "versions": []
}