# A note on the second Gaussian curvature of the helicoidal surfaces

• Cho, Bong-Sik (Division of Mathematics and Informational Statistics, Wonkwang University) ;
• Seo, You-Mi (Division of Mathematics and Informational Statistics, Wonkwang University)
• Published : 2003.03.01

#### Abstract

We define the second Gausssian curvature $K_{II}$ by using Brioschi's formula and shall disscuss the helicoidal surfaces satisfying $K_{II}$=Η.

#### References

1. Arch. Math. v.68 On the inner curvature of the second fundamental form of helicoidal surfaces Baikoussis, C.;Koufogiorgos, T.
2. Geom. J. v.63 Helicoidal surfaces with prescribed mean Gaussian curvature Baikoussis, C.;Koufogiorgos, T.
3. Monatoh. Math. v.113 Ruled surfaces with vanishing second Gauussian curvature Blair, D. E.;Koufogiorgos, T.
4. Tohoku Math. J. v.34 Helicoidal surfaces with constant mean curvature Do Carmo, M.;Dajczer, M.
5. Modern Differential Deometry of Curves and Surfaces Gray, A
6. Proc. Amer. Math. Soc. v.67 A characteristic property of the sphere Hasanis, T.;Koufogiorgos, T.