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Chapter 10: Q3P (page 513)

Show that 未ij系klmis an isotropic tensor of rank 5. Hint: Combine equations (5.4) and (5.7).

Short Answer

Expert verified

The expression未ij鈭�klm is an isotropic tensor.

Step by step solution

01

Given Information

An isotropic tensor of rank 5is .未ij鈭�klm

02

Definition of Isomorphic tensor

Isotropic tensor is defined as a tensor with components that remain unaltered when the coordinate system is rotated arbitrarily.

03

Simplify the isotropic tensor

Use the result given in previous question.

系蚁位蟽'=a蚁ia位ja蟽k系ijk=系蚁位蟽detA=系蚁位蟽

It is known that未伪尾'=未伪尾

Use the above result to get未伪尾'鈭�蚁位蟽'=未伪尾鈭�蚁位蟽

Hence proved that未ij鈭�klm is an isotropic tensor.

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