Pith. sign in

REVIEW 2 cited by

Submersion constructions for geometries with parallel skew torsion

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2409.14421 v1 pith:5V6UU5P2 submitted 2024-09-22 math.DG

Submersion constructions for geometries with parallel skew torsion

classification math.DG
keywords torsiongeometriesmanifoldsparallelholonomyskewsubmersionabsence
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
Share X Bluesky LinkedIn Reddit HN
abstract

In the absence of a de Rham decomposition theorem for geometries with torsion, we develop and unify ways to view a geometry with parallel skew torsion as the total space of a locally defined, not necessarily unique Riemannian submersion with totally geodesic fibers. We complete and extend the Cleyton-Swann classification of irreducible such geometries and characterize the cases where the stabilizer of the torsion is larger than the holonomy. As a byproduct, we obtain structure results on Gray manifolds, nearly parallel G$_2$-manifolds and Sasaki manifolds with reducible holonomy.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

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. ${\mathrm G}_2$-structures with parallel skew-symmetric torsion

    math.DG 2025-10 unverdicted novelty 6.0

    Classification of 7D Riemannian manifolds with parallel skew-symmetric torsion and G2-holonomy, up to naturally reductive spaces and nearly parallel G2-structures, extending Friedrich's cocalibrated work.