Course Details
Subject {L-T-P / C} : MA5111 : Differential Geometry { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Dr. Bikramaditya Sahu
Syllabus
Definition of Space Curve, Arc length, Tangent, Normal, Binormal, Tangent and Osculating Plane, Principal Normal and Binormal, Curvature and Torsion, Serret-Frenet formulae, Curves on a surface, Contact between curves and Surfaces, Osculating Circle and Osculating Sphere, Tangent Surfaces, Involutes and Evolutes,
Intrinsic equation of space curves, Fundamental existence theorems for space curves, Surface representation, Regular and Singular points, Change, Tangent plane and normal, Surfaces of Revolution, Metric on a Surface-The first fundamental form, Invariance of the metric, Direction coefficients on a Surface, Double family of
curves, Isometric correspondence, Intrinsic properties, Geodesics and their Differential Equations, Canonical Geodesic equations, Geodesics on a surface of revolution, Gauss-Bonnet theorem, Second fundamental form, Gauss and Weingarten equations.
Course Objectives
- The objective of the course is to make the students go a step further from multivariable calculus.
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Course Outcomes
The students can venture into the course on Differentiable Manifolds, a more abstract approcah to this study.
Essential Reading
- A. N. Pressely, Elementary Differential Geometry, Springer, 2012.
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Supplementary Reading
- J.A. Thorpe, Elementary Topics in Differential Geometry, Springer, 2004.
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