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.
Pluriclosed manifolds with parallel Bismut torsion
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
abstract
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.
citation-role summary
background 1
citation-polarity summary
fields
math.DG 3verdicts
UNVERDICTED 3roles
background 1polarities
background 1representative citing papers
Riemannian manifolds with a closed parallel torsion 3-form are locally N × G (G semisimple), enabling simplified proofs and explicit classification of strong G2, Spin(7), and certain 8D HKT manifolds.
The paper establishes a canonical reduction theorem and classifies complete simply-connected Bismut-Ambrose-Singer manifolds in homogeneous settings plus their pluriclosed variants.
citing papers explorer
-
Geometries with parallel, skew-symmetric and closed torsion
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.
-
On the rigidity of special and exceptional geometries with torsion a closed $3$-form
Riemannian manifolds with a closed parallel torsion 3-form are locally N × G (G semisimple), enabling simplified proofs and explicit classification of strong G2, Spin(7), and certain 8D HKT manifolds.
-
On Bismut--Ambrose--Singer manifolds
The paper establishes a canonical reduction theorem and classifies complete simply-connected Bismut-Ambrose-Singer manifolds in homogeneous settings plus their pluriclosed variants.