Course

M310 - Geometry of curves and surfaces

Course No: 
M310
Credit: 
4
Prerequisites: 
M306
Approval: 
2014
UG-Core
Syllabus: 
Curves in two and three dimensions, Curvature and torsion for space curves, Existence theorem for space curves, Serret-Frenet formula for space curves, Jacobian theorem, Surfaces in R 3 as 2-dimensional manifolds, Tangent spaces and derivatives of maps between manifolds, Geodesics, First fundamental form, Orientation of a surface, Second fundamental form and the Gauss map, Mean curvature, Gaussian Curvature, Differential forms, Integration on surfaces, Stokes formula, Gauss-Bonnet theorem.
Text Books: 
  1. M. P. Do Carmo, “Differential Geometry of Curves and Surfaces”, Prentice Hall, 1976.
  2. Andrew Pressley, “Elementary Differential Geometry”, Springer, 2010.
Reference Books: 
  1. M. P. Do Carmo, “Differential Forms and Applications”, Springer, 1994.
  2. J. A. Thorpe, “Elementary Topics in Differential Geometry”, Undergraduate texts in mathematics, Springer, 2011.

Contact us

School of Mathematical Sciences

NISERPO- Bhimpur-PadanpurVia- Jatni, District- Khurda, Odisha, India, PIN- 752050

Tel: +91-674-249-4081

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