Write down the transformation laws of the tensors: \\(A_{ijk}^i\\), \\(B_{ijk}^{mn}\\) and \\(C^m\\).
JU-PHY2nd YearFinalMathematical PhysicsTensor AnalysisContra variant and covariant tensors (Topic Practice)JU-PHY - ⚡ অনলাইন প্রশ্নব্যাংক দেখুন 💥
Another Explanation (5):
| Tensor | Transformation Law |
|---|---|
| \(A_{ijk}^i\) | \(A'_{ijk}^i = \frac{\partial x^i}{\partial x'^l} \frac{\partial x'^m}{\partial x^j} \frac{\partial x'^n}{\partial x^k} \frac{\partial x'^p}{\partial x^i} A_{mnp}^l\) |
| \(B_{ijk}^{mn}\) | \(B'_{ijk}^{mn} = \frac{\partial x'^p}{\partial x^i} \frac{\partial x'^q}{\partial x^j} \frac{\partial x'^r}{\partial x^k} \frac{\partial x^m}{\partial x'^s} \frac{\partial x^n}{\partial x'^t} B_{pqr}^{st}\) |
| \(C^m\) | \(C'^m = \frac{\partial x'^m}{\partial x^n} C^n\) |