Geodesic
Surfaces of characteristic curvature
Applications of Mathematics, Tome 19 (1974) no. 1, pp. 36-48
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The paper presents the deduction of the equations of surfaces between the principal curvatures of which the defined relation is valid. This relation represents the characteristic curvature of the surface. The differential equation of the surface of characteristic curvature in Cartesian coordinates is deduced in Section 1 for the case that the ratio between the principal curvatures is constant. Some properties of this surface are given in Section 2. In Section 3 the differential equation of the meridian of a rotary surface of characteristic curvature is deduced. Particular cases of this equation are solved in Section 4. In Section 5 the author deduces parametric equations of the meridian of the rotary surface using the first integral of differential equation; in Section 6 he demonstrates their practical application to technology.
The paper presents the deduction of the equations of surfaces between the principal curvatures of which the defined relation is valid. This relation represents the characteristic curvature of the surface. The differential equation of the surface of characteristic curvature in Cartesian coordinates is deduced in Section 1 for the case that the ratio between the principal curvatures is constant. Some properties of this surface are given in Section 2. In Section 3 the differential equation of the meridian of a rotary surface of characteristic curvature is deduced. Particular cases of this equation are solved in Section 4. In Section 5 the author deduces parametric equations of the meridian of the rotary surface using the first integral of differential equation; in Section 6 he demonstrates their practical application to technology.
DOI : 10.21136/AM.1974.103512
Classification : 53A05 
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Fiřt, Vladimír. Surfaces of characteristic curvature. Applications of Mathematics, Tome 19 (1974) no. 1, pp. 36-48. doi: 10.21136/AM.1974.103512

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