Covariant Differential
The following sections are included:
Fat de Rham Complexes
Fat forms
Semi-fat Forms
Thickened Forms
Geometric Description
Wedge Products
Exterior Fat and Semi-fat Differential
Leibnitz Rule for Fat and Semi-fat Forms
Covariant Differential
Splitting of First Order Jets
Dioles
Multiplication by End(P)–valued Forms
The Square of the Covariant Differential
Leibnitz Rule for the Covariant Differential
Generalization to End(P)–valued Forms
Bianchi Identity
Compatible Linear Connections
cd-Algebras and cd-Modules
Linear Connections and cd-Module Structures on Thickened Forms
Homomorphisms of Thickened Forms Induced by Fat Maps
Geometrical Interpretation of the Induced Homomorphism of Thickened Forms
Compatible Linear Connections
Induced Linear Connections
Lift and Parallel Translation for Arbitrary Smooth Curves
Holonomy
Another Description of Compatibility
Linear Connections Along Fat Maps
Thickened Forms Along Fat Maps
Insertion of D(M)f into
Linear Connections Along Fat Maps
Geometric Description of Linear Connections Along Fat Maps
Covariant Differential Along a Fat Map
Linear Connections Along Maps Associated with Ordinary Linear Connections
Characterization of Compatibility by Means of Associated Linear Connections
Geometric Characterization of Compatibility
Equivalent Conditions for Compatibility
Covariant Lie Derivative
Smooth Families of Fat Maps
Lift of One-parameter Families
Standard Fat Field on a Relative Fat Interval
Geometric Interpretation of the Covariant Derivative
Local Thickened Forms
Time-dependent Thickened Forms
Derivation of Time-dependent Thickened Forms
Lie Derivative Along Fat Fields
Covariant Lie Derivative
Natural Actions on the Space of Linear Connections
Gauge/Fat Structures and Linear Connections
Gauge/Fat Structures
Graded Differential Operators
Λ-Extension of scalars
