Parallel Hypersurfaces in 𝔼^4 and Their Applications to Rotational Hypersurfaces

OpenAlex İngilizce

This study explores parallel hypersurfaces in four-dimensional Euclidean space E4, deriving explicit expressions for their Gaussian and mean curvatures in terms of the curvature functions of the base hypersurface. We identify conditions under which these parallel hypersurfaces are flat or minimal. The theory is applied to several key hypersurfaces, including rotational hypersurfaces, hyperspheres, catenoidal hypersurfaces, and helicoidal hypersurfaces, with detailed curvature computations and visualizations. These results not only extend classical curvature relations into higher-dimensional spaces but also offer valuable insights into curvature transformations, with practical applications in both theoretical and computational geometry.