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arxiv: math/0107101 · v1 · submitted 2001-07-13 · 🧮 math.DG

Stable forms and special metrics

Nigel Hitchin This is my paper
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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