Vanishing theorems of the basic harmonic forms on a complete foliated Riemannian manifold
Seoung Dal Jung, Huili Liu
TL;DR
This paper extends vanishing theorems for basic harmonic forms from compact to complete foliated Riemannian manifolds under certain curvature conditions, broadening the understanding of harmonic forms in geometric analysis.
Contribution
It generalizes existing vanishing theorems to complete foliated Riemannian manifolds, relaxing the compactness requirement.
Findings
Vanishing of basic harmonic forms under transversal curvature conditions
Extension of compact case results to complete manifolds
Broader applicability of harmonic form theorems in foliation geometry
Abstract
On a compact foliated Riemannian manifold with some transversal curvature conditions, there are no nontrivial basic harmonic forms (M. Min-Oo et al., J. Reine Angew. Math. 415 (1991). In this paper, we extend the above facts to a complete foliated Riemannian manifold.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Differential Geometry Research