I read some books and see that the definition of covariant tensor and contravariant tensor.(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# What different between covariant metric tensor and contravariant metric tensor

Loading...

Similar Threads for different between covariant | Date |
---|---|

I Difference between vectors and one-forms | Aug 30, 2017 |

I Difference between diffeomorphism and homeomorphism | Aug 18, 2017 |

I Difference between 1-form and gradient | Feb 6, 2017 |

Difference between covariant and contravariant levi-civita tensor? | Sep 10, 2010 |

Intuitively what's the difference between Lie Derivative and Covariant Derivative? | Feb 5, 2007 |

**Physics Forums - The Fusion of Science and Community**