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arxiv: 2406.07039 · v2 · submitted 2024-06-11 · 🧮 math.DG · math.CV

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Pluriclosed manifolds with parallel Bismut torsion

Giuseppe Barbaro , Francesco Pediconi , Nicoletta Tardini
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classification 🧮 math.DG math.CV
keywords torsionbismutmanifoldsparallelpluriclosedcalabi-yauclassificationcompact
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We present a complete classification of simply-connected pluriclosed manifolds with parallel Bismut torsion, extending previously known results in the literature. Consequently, we also establish a splitting theorem for compact manifolds that are both pluriclosed with parallel Bismut torsion and Calabi-Yau with torsion.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Geometries with parallel, skew-symmetric and closed torsion

    math.DG 2026-05 unverdicted novelty 7.0

    PSCT manifolds locally split into products of well-understood factors for complete local classification, with analysis of almost Hermitian G-structures in Gray-Hervella classes.

  2. On Bismut--Ambrose--Singer manifolds

    math.DG 2026-05 unverdicted novelty 6.0

    The paper establishes a canonical reduction theorem and classifies complete simply-connected Bismut-Ambrose-Singer manifolds in homogeneous settings plus their pluriclosed variants.