General covariant transformations

<p>In <a href="/facts/Physics/a7aH2y08">physics</a>, general covariant transformations are <a href="/facts/Symmetry/hpu7DK8p">symmetries</a> of <a href="/facts/Gravitation/bqAN7DdQ"> gravitation theory</a> on a <a href="/facts/World_manifold/VTwqC8t6">world manifold</a> 
  
    
      
        X
      
    
    {\displaystyle X}
  
. They are <a href="/facts/Gauge_symmetry_(mathematics)/AK834LYK">gauge transformations</a> whose parameter functions are <a href="/facts/Vector_field/ccFNuPPp">vector fields</a> on 
  
    
      
        X
      
    
    {\displaystyle X}
  
. From the physical viewpoint, general covariant transformations are treated as particular (<a href="/facts/Holonomic_function/eaVU0RNs">holonomic</a>) <a href="/facts/Frame_of_reference/15yYfB9M">reference frame</a> transformations in <a href="/facts/General_relativity/jVsoIg8X">general relativity</a>. In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, general covariant transformations are defined as particular <a href="/facts/Automorphisms/WnyxNFkQ">automorphisms</a> of so-called natural <a href="/facts/Fiber_bundle/SJ7Ek6cI">fiber bundles</a>. 
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General covariant transformations open-in-new

General covariant transformations