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Title: Differential Geometry (Code–09050304)

B.Sc. (Hons), Semester-III

S.No. Topic Domain Hours as per UGC
1 One parameter family of surfaces: Envelope, Characteristics, Edge of regression

Developable surfaces, Developable associated with a curve

Osculating developable, Polar Developable, Rectifying developable

Must know 14
2 Two – parameter family of surfaaces

Characteristics Points

Curvilinearcoordinates, First order magnitudes

Directions on a surface, the normal

Second order magnitudes, Derivatives of n

Must know 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

Must know 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

DEL-g , other formulae for DEL-g

Bonnet’s formula

Nice to know 14


Books Recommended:

  1. Weatherburn, C.E., Differential Geometry of Three Dimensions, Radhe Publishing House.
  2. Erwin Kreyszig, Differential Geometry.
  3. Singh, A.K., Mittal, P.K., A Textbook of Differential Geometry, Har-Anand Publications.