60. Principal Normal Line and Osculating Plane

#bsmaths #mscmaths #differentialgeometry Chapter 4 Curvature and Torsion : Principal Normal Line and Osculating Plane

---------------------------------------------------------%%%%%%%%%%%%%%%%%%%%%------------------------------------------ Introduction Theory of Space Curves • Introduction, index notation and summation convention • Space curves, arc length, tangent, normal and binormal • Osculating, normal and rectifying planes • Curvature and torsion • The Frenet-Serret theorem • Natural equation of a curve • Involutes and evolutes, helices • Fundamental existence theorem of space curves Theory of Surfaces • Coordinate transformation • Tangent plane and surface normal • The first fundamental form and the metric tensor • Christoffel symbols of first and second kinds • The second fundamental form • Principal, Gaussian, mean, geodesic and normal curvatures • Gauss and Weingarten equations • Gauss and Codazzi equations Recommended Books

1. R. S. Millman and G.D. Parker, Elements of Differential Geometry (Prentice-Hall, New Jersey, 1977).
2. A. Goetz, Introduction to Differential Geometry (Addison-Wesley, 1970).
3. E. Kreyzig, Differential Geometry (Dover, 1991).
4. M. M. Lipschutz, Schaum's Outline of Differential Geometry (McGraw Hill, 1969).
5. D. Somasundaram, Differential Geometry (Narosa Publishing House, New Delhi, 2005). ... https://www.youtube.com/watch?v=cd3A0zgl9-I