As the title “GEOMETRICAL ANALYSIS IN RIEMANNIAN AND WEYL SPACE” is concerned, geometrical representation of Riemannian and Weyl space has been presented here in respect of general relativity. With a brief notion of Vector & Tensor and Manifolds in first two chapters,different theorems such as Focusing theorem, Forbenius theorem and Raychowdhury equation with some physical interpretation are explained in case of time like geodesic in chapter three.In chapter four,concept of geometry on hypersurface is stated with some recent flavor that includes extrinsic as well as intrinsic curvature.Weyl geometry in the context of recent higher dimensional theorems of space time is discussed in chapter five.Mechanism of embedding of Riemannian space time in Weyl bulk,the problem regarding classical confinement & the stability of motion of particle or photon in the neighborhood of brane when Weyl bulk possess the geometry of warped product space are also discussed. Finally, the only physically reasonable rotating solution (Kerr solution) of Einestein field equation is explained in chapter six which contains a systematic development of different calculations and combinations that lead to the required Kerr solution in Boyer-Lindquist form.
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