Solutions of Exercises of Principles of Tensor Calculus by Taha Sochi
Author:Taha Sochi [Sochi, Taha]
Language: eng
Format: epub
Publisher: UNKNOWN
Published: 2018-10-31T04:00:00+00:00
The vector triple product of a contravariant vector A and two covariant vectors B and C is given by: A × (B × C) =
ϵilmϵjklAiBjCkEm
What is the relation between the relative and absolute permutation tensors in their covariant and contravariant forms?
Answer: The covariant absolute permutation tensor εi1…in is equal to the covariant relative permutation tensor ϵi1…in times √(g), that is: εi1…in = √(g) ϵi1…in
where g is the determinant of the covariant metric tensor.
The contravariant absolute permutation tensor εi1…in is equal to the contravariant relative permutation tensor ϵi1…in divided by √(g), that is: εi1…in = [1 ⁄ √(g)]ϵi1…in
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