### MA2070 Differential Geometry of Curves and Surfaces - [Batches earlier to 2024 only]

#### Course Details

Curves in the Plane and in Space; Arc-Length; Reparametrization; Curvature; The Isoperimetric Inequality; The Four Vertex Theorem Surfaces in Three Dimensions; Tangents, Normals and Orientability; The First Fundamental Form; Lengths of Curves on Surfaces; Equiareal Maps and a Theorem of Archimedes The Second Fundamental Form; Curvature of Curves on a Surface; The Normal and Principal Curvatures; Geometric Interpretation of Principal Curvatures Gaussian and Mean Curvatures and the Gauss Map; Flat Surfaces; Gaussian Curvature of Compact Surfaces Geodesics; Geodesic Equations; Geodesics on Surfaces of Revolution; Geodesics as Shortest Paths; Geodesic Coordinates Gauss's Theorema Egregium; Isometries of Surfaces; The Gauss-Bonnet Theorem for Simple Closed Curves, for Curvilinear Polygons and for Compact Surfaces

#### Course References:

**Text:**

Pressley, Andrew: Elementary differential geometry, Springer undergraduate mathematics series, First Edition, 2001, Chapters 1 to 8, 10 and 11

**References:**

1. Pressley, Andrew: Elementary differential geometry, Enlarged Second Edition, Springer, 2010. 2)

2. Widder, David: Advanced Calculus, Dover Publications, 1989

**Prerequisite:**

Familiarity with Calculus of several variables and matrices