Parallel Hypersurfaces in 𝔼 4 and Their Applications to Rotational Hypersurfaces

Sezgin Büyükkütük, Ilim Kişi, Günay Öztürk and Emre Kişi ()
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Sezgin Büyükkütük: Department of Mechanics, Kocaeli University, 41650 Kocaeli, Türkiye
Ilim Kişi: Department of Mathematics, Kocaeli University, 41380 Kocaeli, Türkiye
Günay Öztürk: Department of Mathematics, Izmir Democracy University, 35140 Izmir, Türkiye
Emre Kişi: Department of Mathematics, Sakarya University, 54187 Sakarya, Türkiye

Mathematics, 2025, vol. 13, issue 22, 1-14

Abstract: This study explores parallel hypersurfaces in four-dimensional Euclidean space E 4 , 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.

Keywords: catenoidal hypersurface; helicoidal hypersurface; parallel hypersurface; rotational hypersurface (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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