The Journal of the Indian Mathematical Society

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


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1 University of Delhi, India
     

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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.


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

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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.