Newton-Cartan connections with torsion
T.Dereli (Koc U.), S.Kocak (Anadolu U.), M.Limoncu (Anadolu U.)
TL;DR
This paper revisits the mathematical framework of Newton-Cartan manifolds, focusing on the compatibility of connections with torsion within this geometric structure, aiming to clarify foundational aspects.
Contribution
It provides a new formulation of Newton-Cartan manifolds and clarifies the conditions for connections with torsion to be compatible with the structure.
Findings
Reformulation of Newton-Cartan manifolds
Clarification of compatibility conditions for torsion connections
Enhanced understanding of geometric structures in non-relativistic gravity
Abstract
We re-formulate the notion of a Newton-Cartan manifold and clarify the compatibility conditions of a connection with torsion with the Newton-Cartan structure.
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Taxonomy
TopicsAdvanced Differential Geometry Research · Relativity and Gravitational Theory · Black Holes and Theoretical Physics