connection on a fiber bundle
C45572
concept
A connection on a fiber bundle is a geometric structure that specifies how to consistently differentiate or "transport" fibers along paths in the base space, thereby splitting motions into horizontal and vertical components.
All labels observed (3)
| Label | Occurrences |
|---|---|
| connection on a fiber bundle canonical | 1 |
| matrix-valued Berry connection | 1 |
| projectively flat connection | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: connection on a fiber bundle
Generated description
A connection on a fiber bundle is a geometric structure that specifies how to consistently differentiate or "transport" fibers along paths in the base space, thereby splitting motions into horizontal and vertical components.
Instances (3)
| Instance | Via concept surface |
|---|---|
| Ehresmann connection | — |
| Hitchin connection | projectively flat connection |
| non-Abelian Berry connection | matrix-valued Berry connection |