2025/07/23 by Vicente Cortés, Cortés, Vicente, Matas Mackevicius +5 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #53D18 (Generalized geometry a la Hitchin) #83C10 (Equations of motion in general relativity and gravitational theory) #Advanced Differential Geometry Research #Control and Dynamics of Mobile Robots #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.2507.17604
openalex publication_date 2025/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a (semi-Riemannian) generalised metric \mathcal G and a divergence operator div on an exact Courant algebroid E, we geometrically construct a canonical generalised Levi-Civita connection D\mathcal G, div for these data. In this way we provide a resolution of the problem of non-uniqueness of generalised Levi-Civita connections. Since the generalised Riemann tensor of D\mathcal G, div is an invariant of the pair (\mathcal G, div), we no longer need to discard curvature components which depend on the choice of the generalised connection. As a main result we decompose the generalised Riemann curvature tensor of D\mathcal G, div in terms of classical (non-generalised) geometric data. Based on this set of master formulas we derive a comprehensive curvature tool-kit for applications in generalised geometry. This includes decompositions for the full generalised Ricci tensor, the generalised Ricci tensor, and three generalised scalar-valued curvature invariants, two of which are new.