Ramanujan Institute for Advanced Study in Mathematics
                                  University of Madras
                                         Syllabus
             MSI C014  Differential Geometry                       3 1 0 4
            Pre-requisite: MSI C002 and MSI C006
           Course Objective : To give a modern introduction to differential geometry of curves and
                          surfaces.
           Unit I
                     3
           Curves in R, Tangent , normal and binormal vectors, curvature and torsion , Plane
           curves.
           Unit II
           Smooth surfaces, Examples of Smooth surfaces,  tangent and normal  vectors,  first
           fundamental form.
           Unit III
           Differential derivative of vector fields, computation of Christoffel symbols, Length and
           Area, Isometries.
           Unit IV
           Weingarten map and the second fundamental form, Gaussian and mean curvatures.
           Unit V
           Gauss formula, Gauss equation,  Codazzi-Mainardi Equations, Theorema  Egregium .
           References :
           1. Ethan  D.  Block,  first  course  in  geometric  topology  and  differential  geometry,
              Birkhauser.
           2. Andrew  Pressley,  Elementary  differential  geometry,  Springer  Undergraduate
              Mathematics series.