Page 280 - DMTH402_COMPLEX_ANALYSIS_AND_DIFFERENTIAL_GEOMETRY

Unit 22: Bertrand Curves

22.7 Self Assessment Notes

1. If n  4, then no C -special Frenet curve in E is a ................
n

1. In the case of ................ the Frenet 1-normal vector fields n1 is already called the principal
normal vector field along C, and the Frenet 1-normal line is already called the principal
normal line of C at c(s).
3. A C -special Frenet curve in E with 1-curvature function k and 2-curvature function k is
3

2
1
a Bertrand curve if and only if there exists a linear relation ................ for all s  L, where a
and b are nonzero constant real numbers.
4. Let C be a Bertrand curve in En (n  4) and C a ................ of C. C is distinct from C.
22.8 Review Questions

1. Discuss Special Frenet Curves in E n
2. Describe Bertrand Curves in E n
3. Explain (1, 3)-Bertrand Curves in E 4

Answers: Self Assessment

1. Bertrand curve. 2. Euclidean 3-space,
3. ak (s) + bk (s) = 1 4. Bertrand mate
2
1
22.9 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 273