Construction of Transverse Metrics from Transversely Elliptic Operators on Foliated Manifolds
Wenran Liu
Abstract
The existence of a transverse metric on a foliated manifold is typically used as a framework for studying transversely elliptic basic differential operators. This article details a method for constructing such a transverse metric directly from the principal symbol of the operator. Consequently, rather than treating the transverse metric as a mere working assumption, we demonstrate that its existence is a necessary condition for the very presence of a transversely elliptic operator.
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