Differential Geometry-I
Paper Code:
MAT124
Credits:
5
Contact Hours:
75.00
Max. Marks:
100.00
Unit I:
I
15.00
Theory of curves- Space curves, Tangent, Contact of curve and surface, Osculating plane, Principal normal and Binormal, Curvature, Torsion, Serret-Frenet's formulae.
Unit II:
II
15.00
Osculating circle and Osculating sphere, Existence and Uniquenss theorems, Bertrand curves, Involute, Evolutes.
Unit III:
III
15.00
Ruled surface, Developable surface, Tangent plane to a ruled surface. Necessary and sufficient condition that a surface ℑ=f () should represent a developable surface.
Unit IV:
IV
15.00
Metric of a surface, First, second and third fundamental forms. Fundamental magnitudes of some important surfaces, Orthogonal trajectories. normal curvature, Meunier's theorem,.
Unit V:
V
15.00
Principal directions and Principal curvatures, First curvature, Mean curvature, Gaussion curvature. Umbilics. Radius of curvature of any normal section at an umbilic on z = f(x,y). Radius of curvature of a given section through any point on z = f(x,y). Lines of curvature, Principal radii, Relation between fundamental forms. Asymptotic lines.
Essential Readings:
- Thorpe, ‘Elementary Topics in Differential Geometry’, Second Edition, Springer Verlag, New York, (1985).
- J.L.Bansal & P.R.Sharma, Differential Geometry,JPH,Jaipur
- Raj Bali, Differential Geometry, Navkar Publication, Ajmer
References:
- T.J.Willmore, ‘An Introduction to Differential Geometry’, Oxford University Press, London, (1972).
- Dirk J. Struik, ‘Lectures on Classical Differential Geometry’, Second Edition, Addison Wesley Publishing Company, London, (1961).
Academic Year:
