Abstract
We define helical (i.e., helicoidal) hypersurfaces depending on the axis of rotation in Minkowski four-space E 1 4 . There are three types of helicoidal hypersurfaces. We derive equations for the curvatures (i.e., Gaussian and mean) and give some examples of these hypersurfaces. Finally, we obtain a theorem classifying the helicoidal hypersurface with timelike axes satisfying Δ I H = A H .
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Reference32 articles.
1. Total Mean Curvature and Submanifolds of Finite Type;Chen,1984
2. Minimal immersions of Riemannian manifolds
3. On a Certain Class of Conformally at Euclidean Hypersurfaces;Ferrandez,1991
4. Characterization of the helicoid as ruled surfaces with pointwise 1-type Gauss map;Choi;Bull. Korean Math. Soc.,2001
5. On surfaces of finite type in Euclidean $3$-space
Cited by
15 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献