Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-04-24
Class.Quant.Grav. 18 (2001) 5521-5544
Physics
High Energy Physics
High Energy Physics - Theory
29 pages, no figure; (v2) Errors are corrected ; (v3) Some explanations are added. More general differential equations for SU(
Scientific paper
10.1088/0264-9381/18/24/314
We study Ricci-flat metrics on non-compact manifolds with the exceptional holonomy $Spin(7), G_2$. We concentrate on the metrics which are defined on ${\bf R} \times G/H$. If the homogeneous coset spaces $G/H$ have weak $G_2$, SU(3) holonomy, the manifold ${\bf R} \times G/H$ may have $Spin(7), G_2$ holonomy metrics. Using the formulation with vector fields, we investigate the metrics with $Spin(7)$ holonomy on ${\bf R}\times Sp(2)/Sp(1), {\bf R}\times SU(3)/U(1)$. We have found the explicit volume-preserving vector fields on these manifold using the elementary coordinate parameterization. This construction is essentially dual to solving the generalized self-duality condition for spin connections. We present most general differential equations for each coset. Then, we develop the similar formulation in order to calculate metrics with $G_2$ holonomy
Konishi Yoshinao
Naka Michihiro
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