Coset Construction of $Spin(7), G_2$ Gravitational Instantons

We study metrics on non-compact manifolds with the exceptional holonomy $Spin(7), G_2$. Using the formulation with vector fields, we investigate the metrics with $Spin(7)$ holonomy recently found by Cveti\v{c}, Gibbons, L\"u and Pope [hep-th/0103155]. Furthermore, we develop the similar formulation for metrics with $G_2$ holonomy.