In this book, we focus on some aspects of vector fields, connections, metrics and tensors, which appear of fundamental importance for the developments of differential geometry and its applications to Theoretical Physics, Special and General Relativity, Economics and Finance. In particular we touch basic topics, for instance: definition of vector fields; smoothness of a vector field; Euclidean connection in Rn; definition of a connection; locality of covariant derivatives; directional derivatives; Christoffel symbols; covariant derivatives chart components; locally flat connections in a chart; parallel transport; metric manifolds; musical isomorphisms and connections.
Differential Geometry and Relativity Theories. Vol.2. Vector fields, connections, metrics, tensors
David Carfì
2021-01-01
Abstract
In this book, we focus on some aspects of vector fields, connections, metrics and tensors, which appear of fundamental importance for the developments of differential geometry and its applications to Theoretical Physics, Special and General Relativity, Economics and Finance. In particular we touch basic topics, for instance: definition of vector fields; smoothness of a vector field; Euclidean connection in Rn; definition of a connection; locality of covariant derivatives; directional derivatives; Christoffel symbols; covariant derivatives chart components; locally flat connections in a chart; parallel transport; metric manifolds; musical isomorphisms and connections.Pubblicazioni consigliate
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