论文信息 - Stable forms and special metrics

Stable forms and special metrics

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.

Nigel Hitchin

[1] T. Friedrich,et al. Twistors and killing spinors on riemannian manifolds , 1991 .

[2] Recently D. Joyce. On Nearly Parallel G 2-Structures , 1995 .

[3] W. Reichel. Über trilineare alternierende Formen in sechs und sieben Veränderlichen und die durch sie definierten geometrischen Gebilde , 1907 .

[4] J. A. Schouten. Klassifizierung der alternierenden Gröszen dritten Grades in 7 Dimensionen , 1931 .

[5] T. Friedrich,et al. On nearly parallel G2-structures , 1997 .

[6] A. Gray. Weak holonomy groups , 1971 .

[7] A. Gray,et al. Riemannian manifolds with structure groupG2 , 1982 .

[8] Nigel Hitchin,et al. THE GEOMETRY OF THREE-FORMS IN SIX DIMENSIONS , 2000 .

[9] Christian Bär. Real Killing spinors and holonomy , 1993 .

[10] E. Rees,et al. Compact 3-Sasakian 7-manifolds with arbitrary second Betti number , 1998 .

[11] S. Salamon. Riemannian geometry and holonomy groups , 1989 .