The Journal of the Indian Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

Comparison of Sannia's Theory of Line Congruences With Gauss's Theory of Surfaces


Affiliations
1 University of Delhi, India
     

   Subscribe/Renew Journal


The relation between the theory of line congruences and Gauss's theory of surfaces has been noted by Kummer. He mentions the analogy between Hamilton's formula p = p1 cos2θ + p2 sin2θ and Euler's formula 1/R = cos2θ/R1+sin2θ/R2. The analogy between the total and mean curvatures of the surface, and the total and mean parameters of the congruence and some other analogies have been mentioned by Sannia.

The object of this paper is to point out some other similarities between the two theories.


Subscription Login to verify subscription
User
Notifications
Font Size


Abstract Views: 199

PDF Views: 0




  • Comparison of Sannia's Theory of Line Congruences With Gauss's Theory of Surfaces

Abstract Views: 199  |  PDF Views: 0

Authors

Ram Behari
University of Delhi, India

Abstract


The relation between the theory of line congruences and Gauss's theory of surfaces has been noted by Kummer. He mentions the analogy between Hamilton's formula p = p1 cos2θ + p2 sin2θ and Euler's formula 1/R = cos2θ/R1+sin2θ/R2. The analogy between the total and mean curvatures of the surface, and the total and mean parameters of the congruence and some other analogies have been mentioned by Sannia.

The object of this paper is to point out some other similarities between the two theories.