Curvature and Weitzenböck formula for spectral triples
Year: 2024
Type: article
Abstract: Using the Levi‐Civita connection on the noncommutative differential 1‐forms of a spectral triple , we define the full Riemann curvature tensor, the Ricci curvature tensor and scalar curvature. We give a definition of Dirac spectral triples and derive a general Weitzenböck formula for them. We apply these tools to ‐deformations of compact Riemannian manifolds. We show that the Riemann and Ricci tensors transform naturally under ‐deformation, whereas the connection Laplacian, Clifford representation of the curvature, and the scalar curvature are all invariant under deformation.
Source: Mathematische Nachrichten
Authors: Bram Mesland, Adam Rennie
Institutions: Leiden University, University of Wollongong
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,300
OpenAlex ID: W4403260108