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.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1249-1275
Launched on MUSE
1996-12-01
Open Access
No
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