Related Structures
The smoothness requirements on the transition functions can be weakened, so that we only require the transition maps to be k-times continuously differentiable; or strengthened, so that we require the transition maps to real-analytic. Accordingly, this gives a or (real-)analytic structure on the manifold rather than a smooth one. Similarly, we can define a complex structure by requiring the transition maps to be holomorphic.
Read more about this topic: Smooth Structure
Famous quotes containing the words related and/or structures:
“In the middle years of childhood, it is more important to keep alive and glowing the interest in finding out and to support this interest with skills and techniques related to the process of finding out than to specify any particular piece of subject matter as inviolate.”
—Dorothy H. Cohen (20th century)
“If there are people who feel that God wants them to change the structures of society, that is something between them and their God. We must serve him in whatever way we are called. I am called to help the individual; to love each poor person. Not to deal with institutions. I am in no position to judge.”
—Mother Teresa (b. 1910)