Riemannian Velocity and Acceleration Tensors/Vectors in Rotational Oblate Spheroidal Coordinates Based Upon the Great Metric Tensor

Abstract

Since the time of Galileo (1564 - 1643), Euclidean geometry has been the foundation on which the theoretical formulations of all geometrical quantities in all orthogonal curvilinear coordinates in Physics and Mathematics were built. But with the discovery of the great metric tensor in spherical polar coordinates  in all gravitational fields in nature[5] has made Riemannian geometry to be opened up for exploration and exploitation and hence its application in Theoretical Physics and Mathematics. In this paper, we derive the Riemannian vector and acceleration tensor/vectors in Rotational Oblate Spheroidal coordinates for application in physics and other related fields.