Analysis of the Horizontal Laplacian for the Hopf Fibration

Abstract

We study the horizontal Laplacian ∆ associated to the Hopf fibration S → S with arbitrary Chern number k. We use representation theory to calculate the spectrum, describe the heat kernel and obtain the complete heat trace asymptotics of ∆ . We express the Green functions for associated Poisson semigroups and obtain bounds for their contraction properties… (More)

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