**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:**

- 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, Har-Anand Publications.