Abstract:
In this research, we show by using integration of different form that , for a compact
orientable manifold of dimension n the De Rham cohomology group () is non
zero, we also show that the group for a compact , connected , orientable manifold
is just one-dimensional.
We discuss the metric tensor and Riemannian metric on a manifold in informal
terms. We also illustrate the relation between the integral curve of geodesic flow
and geodesic with some examples and applications .