Workshop on Differential Geometry with Tensor Applications

Workshop on Differential Geometry with Tensor Applications

July 27-28, 2019
Department of Mathematics, Universitas Gadjah Mada
Lecturers: :
Dr. Dipankar De


Tensor Analysis deals with the entities and properties that are independent of choice of reference frames, it forms the ideal tool for the study of natural laws. In particular, Einstein found it an excellent tool for presentation of his “General Theory of Relativity”. As a result tensor calculus come into general prominence and is now invaluable in its applications to most branches of theoretical physics, it is also indispensable in the Differential Geometry of curves in space and surfaces in Euclidean space E3. Brief Introduction presents the fundamental theory of curves and surfaces and applies them to number of examples using with tensor calculus. Topic includes tensor calculus, curves, theory of surfaces, fundamental equation, geometry on surface and more.


  1. Tensor
    Scope of tensor analysis,transformation laws,transformation by covariance and contravariance tensor, metric tensors, Christoffels’ symbols, Covariant differentiation tensor and formulas,Ricci tensor, Riemannian and Euclidean space, e-System and Kronecker’s delta.

  2. Curves in space
    Parametric representation of curves, Helix, curvilinear coordinates in E3. First curvature vector, Serret-Frenet formulas for curves in space, Frenet formulas for curve in En. Intrinsic differentiation, Parallel vector fields, Geodesic.

  3. Surfaces
    Parametric representation of a Surface, The first and second fundamental tensor, Geodesic curvature of a surface curve, The third fundamental form, Gaussian Curvature, Isometry of surfaces, Developable surfaces, Weingarten formula, Equation of Gauss and Codazzi, Principal curvature, Normal Curvature. Mean and total Curvatures, Meusnier’s theorem.


International: $ 25
Indonesian Student : Rp 100k
Indonesian Participant : Rp 200k


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