Title Differential Geometry (Code–09050304)
B.Sc. (Hons) Mathematics (3^{rd} Semester)
S.No.  Contents of the topics  Learning Objectives  Teaching Guidelines  Methodology  Time
(Hour) 
1  · One parameter family of surfaces: Envelope,
· Characteristics, Edge of regression · Developable surfaces, Developable associated with a curve · Osculating developable, Polar Developable, Rectifying developable 
Students will be able to understand family of surfaces, Polar Developable, Rectifying developable  Lecture should be effective so that student can grasp the topics easily  Assignments/ seminars/ Class tests/ Presentations  14 
2  · Two – parameter family of surfaces
· Characteristics Points · Curvilinear coordinates, First order magnitudes · Directions on a surface, the normal · Second order magnitudes, Derivatives of n 
Students will be able to understand Two – parameter family of surfaces

Lecture should be effective so that student can grasp the topics easily  Assignments/ seminars/ Class tests/ Presentations  12 
3  · Curves on a surface, Principal directions and curvature
· First and Second curvatures, Euler’s Theorem · Dupin’s indicatrix, The surfaces z = f(x, y) · Surface of revolution, Conjugate directions, Conjugate systems · Asymptotic lines, Curvature and Torsion, Isometric parameters · Null lines, Minimal surfaces 
Students will be able to understand curvatures, Torsion, Minimal surfaces  Lecture should be effective so that student can grasp the topics easily  Assignments/ seminars/ Class tests/ Presentations  10 
4  · Geodesics : Geodesic property, Equation of Geodesics
· Surface of revolution · Torsion of Geodesic · Curves in relation to geodesics · Bonnet”s theorem · Joachimsthal’s Theorems · Vector curvature · Geodesic curvature · DELg , other formulae for DELg · Bonnet’s formula 
Students will be able to understand about Geodesics, Surface of revolution, Torsion of Geodesic and Geodesic curvature  Lecture should be effective so that student can grasp the topics easily  Assignments/ seminars/ Class tests/ Presentations  14 
Books Recommended:
 Weatherburn, C.E., Differential Geometry of Three Dimensions, Radhe Publishing House.
 Erwin Kreyszig, Differential Geometry.
 Singh, A.K., Mittal, P.K., A Textbook of Differential Geometry, HarAnand Publications.