Parallel transports in tensor spaces generated by derivations of tensor algebras
Bozhidar Z. Iliev (Institute for Nuclear Research, Nuclear Energy,, Bulgarian Academy of Sciences, Sofia, Bulgaria)
TL;DR
This paper provides an axiomatic description of parallel transports in tensor spaces generated by derivations of tensor algebras along paths, exploring their properties and applications on differentiable manifolds.
Contribution
It introduces a new axiomatic framework for understanding parallel transports generated by derivations of tensor algebras, extending their analysis on manifolds.
Findings
Properties of these transports are characterized.
Framework applicable to tensor algebra over manifolds.
Abstract
The (parallel linear) transports in tensor spaces generated by derivations of the tensor algebra along paths are axiomatically described. Certain their properties are investigated. Transports along paths defined by derivations of the tensor algebra over a differentiable manifold are considered.
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Taxonomy
Topicsadvanced mathematical theories · Algebraic and Geometric Analysis · Medical Imaging Techniques and Applications