(0,2)-tensor
C3716
concept
A (0,2)-tensor is a bilinear map that takes two vectors as input and returns a scalar, often representing objects like metrics or covariant tensor fields on a vector space or manifold.
All labels observed (6)
| Label | Occurrences |
|---|---|
| bilinear form | 3 |
| (0,2)-tensor canonical | 1 |
| Hermitian form | 1 |
| second fundamental form-related operator | 1 |
| sesquilinear form | 1 |
| symmetric bilinear form | 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: (0,2)-tensor
Generated description
A (0,2)-tensor is a bilinear map that takes two vectors as input and returns a scalar, often representing objects like metrics or covariant tensor fields on a vector space or manifold.
Instances (7)
| Instance | Via concept surface |
|---|---|
| Kähler form | Hermitian form |
| Weil pairing | bilinear form |
| Minkowski metric η_{μν} | bilinear form |
|
Hermitian forms (work on quadratic forms)
surface form:
Hermitian form
|
sesquilinear form |
| Cartan–Killing form | bilinear form |
| shape operator | second fundamental form-related operator |
| Ricci curvature tensor | — |