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The basic Laplacian of a Riemannian foliation. (English) Zbl 0865.58047

Author’s abstract: “We study the basic Laplacian on Riemannian foliations by writing the basic Laplacian in terms of the orthogonal projection from square-integrable forms to basic square-integrable forms. Using a geometric interpretation of this projection, we relate the ordinary Laplacian to the basic Laplacian. Among other results, we show the existence of the basic heat kernel and establish estimates for the eigenvalues of the basic Laplacian”.

MSC:

58J50 Spectral problems; spectral geometry; scattering theory on manifolds
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