In the expression $B_k^{i \cdot m}$, the first, second, and third indices are identified based on the positioning of subscripts and superscripts.

1. First index: $k$, the subscript.
2. Second index: $i$, the first superscript.
3. Third index: $m$, the second superscript (after the dot).

Would you like a more detailed explanation of these types of notations or indices?

Here are 5 related questions that expand on this concept:

1. What is the significance of subscripts and superscripts in tensor notation?
2. How can we interpret the dot between $i$ and $m$ in the given notation?
3. Can this type of indexing notation be extended to higher dimensions?
4. What role do indices play in mathematical operations involving tensors or matrices?
5. How can we simplify or manipulate expressions with multiple indices?

Tip: In tensor algebra, subscripts often denote different dimensions or components, and the position of indices can change the nature of the operations (e.g., summation conventions, transformations).