Curves in two and three dimensions, Curvature and torsion for space
curves, Existence theorem for space curves, Serret-Frenet formula for
space curves, Inverse and implicit function
theorems, Jacobian theorem, Surfaces in R^3 as two dimensional
manifolds, Tangent space and derivative of maps between manifolds, First
fundamental form, Orientation of a surface, Second
fundamental form and the Gauss map, Mean curvature and scalar curvature,
Integration onsurfaces, Stokes formula, Gauss-Bonnet theorem.
Reference Texts:
1. M.P. do Carmo:
Differential Geometry of Curves and Surfaces.
2. A. Pressley: Elementary Differential Geometry.
3. J. A. Thorpe: Introduction to Elementary Differential Geometry.
- Teacher: Suresh Nayak