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Stable forms and special metrics

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arxiv math/0107101 v1 pith:7HF7T453 submitted 2001-07-13 math.DG

Nigel Hitchin This is my paper · ORCID
classification math.DG
keywords metricsdimensionsformsholonomyspecialspinbecomescalculating
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We show how certain diffeomorphism-invariant functionals on differential forms in dimensions 6,7 and 8 generate in a natural way special geometrical structures in these dimensions: metrics of holonomy G2 and Spin(7), metrics with weak holonomy SU(3) and G2, and a new and unexplored example in dimension 8. The general formalism becomes a practical tool for calculating homogeneous or cohomogeneity one examples, and we illustrate this with some newly discovered cases of Spin(7) and G2 metrics.

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Cited by 2 Pith papers

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

  1. The canonical symmetry reduction of string backgrounds

    math.DG 2025-11 conditional novelty 6.0 of 10

    A compact string background with nonvanishing canonical symmetry reduces to a transverse string generalized Ricci soliton that is conformally co-closed, with explicit torsion in SU(3), G2, and Spin(7).

  2. On the Plebanski Formulation with Energy Momentum

    gr-qc 2026-06 unverdicted novelty 3.0 of 10

    Explicit construction of the Plebanski matter source T^i via Kulkarni-Nomizu lifting of the trace-free energy-momentum tensor that reproduces Krasnov's definition and yields the Reissner-Nordström-de Sitter solution.

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