tensor field
C2816
concept
A tensor field is a mathematical object that assigns a tensor (a multilinear map or multidimensional array following specific transformation rules) to every point in a space or manifold, varying smoothly from point to point.
All labels observed (7)
| Label | Occurrences |
|---|---|
| (1,1)-form | 2 |
| spinor field | 2 |
| tensor field canonical | 2 |
| field variable in continuum mechanics | 1 |
| fundamental field | 1 |
| scalar field on a surface | 1 |
| vector field | 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: tensor field
Generated description
A tensor field is a mathematical object that assigns a tensor (a multilinear map or multidimensional array following specific transformation rules) to every point in a space or manifold, varying smoothly from point to point.
Instances (10)
| Instance | Via concept surface |
|---|---|
| Dirac field | spinor field |
| Kähler form | (1,1)-form |
| Maxwell stress tensor | — |
| Cauchy stress tensor | field variable in continuum mechanics |
| Gaussian curvature | scalar field on a surface |
| Higgs field | fundamental field |
| Dirac adjoint field | spinor field |
| Fubini–Study form | (1,1)-form |
| Einstein tensor | — |
| Poynting vector | vector field |