proof that transition functions of cotangent bundle are valid
The first criterion is the easiest to verify. If , then reduces to the identity and we have
Thus we see that is the identity map, as required.
Next, we turn our attention to the third criterion — showing that . For clarity of notation let us define . Then we have
Finally, the second criterion does not need to be checked because it is a consequence of the first and third criteria.
|Title||proof that transition functions of cotangent bundle are valid|
|Date of creation||2013-03-22 14:52:25|
|Last modified on||2013-03-22 14:52:25|
|Last modified by||rspuzio (6075)|