PreprintCC BY 4.0arXiv
Construction of Transverse Metrics from Transversely Elliptic Operators on Foliated Manifolds
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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BibTeX
@misc{liu2026construction,
title = {{Construction of Transverse Metrics from Transversely Elliptic Operators on Foliated Manifolds}},
author = {Wenran Liu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07903},
eprint = {2611.07903},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07903},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Construction of Transverse Metrics from Transversely Elliptic Operators on Foliated Manifolds
AU - Wenran Liu
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07903
UR - https://arxiv.org/abs/2611.07903
AB - 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.
ER -