DIFFERENTIAL GEOMETRY-I
Theory of curves: Space curves, Tangent, Contact of curve and surface, Osculating plane, Principal normal and binormal, Curvature, Torsion, Serret-Frenet's formulae.
Osculating circle and osculating sphere, Existence and uniqueness theorems for space curves, Bertrand curves, Involutes, Evolutes.
Envelops and edge of regression, Ruled surfaces, Developable surfaces, Tangent plane to a ruled surface, Necessary and sufficient condition that a surface ℑ=f (ξ, ƞ) should represent a developable surface, Metric of a surface: First, second and third fundamental forms.
Fundamental magnitudes of some important surfaces, Orthogonal trajectories, normal curvature, Meunier's theorem, 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, Curvature of the normal section.
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- P.P. Gupta & G.S. Malik, Differential Geometry, Pragati Prakashan Meerut, 2012.
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- Raj Bali, Differential Geometry, Navkar Publication, Ajmer, 2012.
- T.J. Willmore, An Introduction to Differential Geometry, Oxford University Press, London, 1972.
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- Erwin Kreyszig, Differential Geometry, Dover Publishing, 1991.
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- Clifford Henry Taube’s, Differential Geometry, Oxford university press, 2011.
- B.D. Neill, Elementary Differential Geometry, Academic Press, London, 1996.
- Nirmala Prakash, Differential Geometry, Tata McGraw Hill, 1981.
- Millan and G.D. Parker, Elements of Differential Geometry, PHI, 1977.
- D. Somasundaram, Differential Geometry, Narosa Publishing House, New Delhi 2005.
