Page 322 - DMTH402_COMPLEX_ANALYSIS_AND_DIFFERENTIAL_GEOMETRY

Unit 25: Curvature

25.6 Self Assessment Notes

1. ...................... refers to any of a number of loosely related concepts in different areas of
geometry.
2. ......................, which is defined at each point in a Riemannian manifold.
3. ...................... defined the center of curvature C as the intersection point of two infinitely
close normals to the curve, the radius of curvature as the distance from the point to C, and
the curvature itself as the inverse of the radius of curvature.

4. The ...................... and normal vector together describe the second-order behavior of a
curve near a point.

25.7 Review Question

1. Discuss the concept of Curvature of plane curves.
2. Explain the Curvature of a graph.
3. Define Signed curvature and discuss it in detail.
4. Describe Curvature of space curves.
5. Explain Curves on surfaces.

Answers: Self Assessment

1. Curvature 2. Intrinsic curvature
3. Cauchy 4. tangent, curvature

25.8 Further Readings

Books Ahelfors, D.V. : Complex Analysis
Conway, J.B. : Function of one complex variable
Pati, T. : Functions of complex variable

Shanti Narain : Theory of function of a complex Variable
Tichmarsh, E.C. : The theory of functions
H.S. Kasana : Complex Variables theory and applications
P.K. Banerji : Complex Analysis

Serge Lang : Complex Analysis
H. Lass : Vector & Tensor Analysis
Shanti Narayan : Tensor Analysis
C.E. Weatherburn : Differential Geometry

T.J. Wilemore : Introduction to Differential Geometry
Bansi Lal : Differential Geometry.

LOVELY PROFESSIONAL UNIVERSITY 315