Course Credit:
4
Geometry of Differential Manifolds is based on three dimensional basic vector geometry of curves and surfaces with calculus. Understanding of this course students will precede to learn other areas of mathematics such as Differentiable Manifolds, Riemannian Manifolds, Theory of Relativity and cosmology etc. Upon the successful completion of this course students will able to apply the concepts of surfaces to find which surface are minimal surfaces and also to know Weingarten, Gauss and Codazzi equations, Theorema Egreegium, fundamental theorem of surface theory etc. Students will know the concepts of developable surfaces, ruled surfaces, Gaussian curvature, Geodesics, Geodesic curvature, Liouvilles formula, Clairaut’s theorem, Bonnet’s formula and Gauss-Bonnet theorem. Students will learn about Conformal, isometric and geodesic mapping, Tissot’s theorem. Theory of differential functions, charts, atlases, differentiable manifolds, smooth map on Manifolds, Tangent space, Tangent bundles, - vector fields and Lie brackets of vector fields on Manifolds, φ - related vector fields.