- #1
HeilPhysicsPhysics
- 16
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I read some books and see that the definition of covariant tensor and contravariant tensor.
Covariant tensor(rank 2)
A'_ab=(&x_u/&x'_a)(&x_v/&x'_b)A_uv
Where A_uv=(&x_u/&x_p)(&x_u/&x_p)
Where p is a scalar
Contravariant tensor(rank 2)
A'^uv=(&x'^u/&x^a)(&x'^v/&x^b)A^ab
Where A^ab=dx_a dx_b
Metric tensor sometimes g^uv,sometimes g_uv
ds^2=g_uv dx^u dx^v=g^uv dx_u dx_v
What different between them?
Covariant tensor(rank 2)
A'_ab=(&x_u/&x'_a)(&x_v/&x'_b)A_uv
Where A_uv=(&x_u/&x_p)(&x_u/&x_p)
Where p is a scalar
Contravariant tensor(rank 2)
A'^uv=(&x'^u/&x^a)(&x'^v/&x^b)A^ab
Where A^ab=dx_a dx_b
Metric tensor sometimes g^uv,sometimes g_uv
ds^2=g_uv dx^u dx^v=g^uv dx_u dx_v
What different between them?