Focal and Generalized Focal Geometry Associated with Rotational Hypersurfaces in E4
Symmetry, cilt.18, ss.1-20, 2026 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 18
- Basım Tarihi: 2026
- Doi Numarası: 10.3390/sym18101673
- Dergi Adı: Symmetry
- Derginin Tarandığı İndeksler: Scopus
- Sayfa Sayıları: ss.1-20
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Kocaeli Üniversitesi Adresli: Evet
Özet
This paper investigates focal and generalized focal geometry associated with rotational
hypersurfaces in the four-dimensional Euclidean space E4. Explicit parametrizations are
derived for several classes of rotational hypersurfaces, including toroidal and special
Monge-type structures. The corresponding focal hypersurfaces are constructed and their
geometric properties are analyzed through the computation of shape operators, Gaussian
curvature, and mean curvature. Conditions for degeneracy, flatness, and minimality are
determined. In addition, generalized focal hypersurfaces defined via principal curvaturedependent offsets are introduced and examined. The results provide explicit geometric desscriptions and curvature characterizations that extend classical focal constructions from E3 to higher-dimensional hypersurface geometry, while highlighting the role of rotational symmetry in the structure and degeneracy of focal hypersurfaces.