Gravitational Instanton - Examples

Examples

It will be convenient to write the gravitational instanton solutions below using left-invariant 1-forms on the three-sphere S3 (viewed as the group Sp(1) or SU(2)). These can be defined in terms of Euler angles by

\sigma_1 = \sin \psi \, d \theta - \cos \psi \sin \theta \, d \phi
\sigma_2 = \cos \psi \, d \theta + \sin \psi \sin \theta \, d \phi
\sigma_3 = d \psi + \cos \theta \, d \phi.

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