MANIFOLDS

Riemann's curvature and manifold are those things which at first site puzzled and shocked everyone. That time of Riemann the interest of everyone in Hyperspace grows really well and they want something which clarify the entire Physical and Mathematical properties. Riemann introduced manifolds which were nothing more than the collection of points which can be in three or more dimensions. His analysis towards the curvatures was very general and beautiful. He thought about a simple triangle which we all know is an object of two dimension. He took that two dimensional object and thought about the changes it holds when it is made upon a sphere. He observe the change that the sum of the angle of the triangle would be greater than 180 degrees he named such manifold as the positive manifold which raises the fundamental Euclid's laws and named as negative manifolds in which the sum in less than 180 degrees. His such Mathematical discoveries really thrilled the world and it is a fact that Einstein General theory of relativity would never be succeed if didn't study the Riemann mathematics because the entire mathematics he used in his GTR was of Riemann. And he was succeeded in finding a physical meaning of that curvature.