TL;DR
This paper introduces a family of Laplacian operators on Riemannian manifolds, unifying various examples and providing a framework for understanding vanishing theorems in differential geometry.
Contribution
It defines a one-parameter family of Laplacians on sections of associated bundles, connecting different instances within a unified framework.
Findings
Unified framework for Laplacians on Riemannian manifolds
Examples of Laplacians fit into the proposed family
Potential applications to vanishing theorems
Abstract
On a Riemannian manifold we define a one-parameter family of Laplacians acting on sections of any bundle associated to the principal frame bundle via a representation, and show how various examples fit into this framework.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Neuroimaging Techniques and Applications · Medical Imaging Techniques and Applications