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The Berger metric on a “squashed” three-sphere is given (in Euler coordinates) by 4 $ ds^2 = \lambda^2 (d \tau + \cos \theta d \phi)^2 + d \theta^2 + \sin^2 \theta d \phi^2$ . See for example Eq. 1.11 of this paper. This formula describes the geodesic distance between two infinitesimally separated points. My question:Read more

Is anything known about the Laplacian on squashed spheres $ S^{2n-1}_\omega$ , where the ambient $ C^n$ coordinates satisfy $ $ 1= \sum_{i=1}^n \omega_i |z_i|^2 $ $ for fixed real numbers $ \omega_i$ ? for example are the eigenvalues or the heat kernel known?Read more