ON A CERTAIN CLASS OF ROTATIONAL HYPERSURFACES SATISFYING ∆x = Ax IN THE SIX-DIMENSIONAL EUCLIDEAN SPACE

Güler E., YAYLI Y., HACISALİHOĞLU H. H.

Romanian Journal of Mathematics and Computer Science, vol.15, no.2, pp.46-54, 2025 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 2
  • Publication Date: 2025
  • Journal Name: Romanian Journal of Mathematics and Computer Science
  • Journal Indexes: Scopus
  • Page Numbers: pp.46-54
  • Keywords: 6-space, curvature, Laplace–Beltrami operator, rotational hypersurface
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

A specific class of rotational hypersurfaces x with five parameters in the six-dimensional Euclidean space E6 is investigated. The curvature functions associated with these hypersurfaces are explicitly computed, and their geometric properties are examined. Furthermore, the action of the Laplace–Beltrami operator on such hypersurfaces is analyzed, and the conditions under which the relation ∆x = Ax holds for a 6 × 6 matrix A are determined.