Surfaces with <i>H</i><SUP>2</SUP> = K along a given curve

Kose B., Bayram E.

FILOMAT, vol.40, no.3, pp.1015-1022, 2026 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 40 Issue: 3
  • Publication Date: 2026
  • Doi Number: 10.2298/fil2603015k
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.1015-1022
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In the present paper, we handle the problem of construction of surfaces with a given curve whose squared mean curvature is equal to the Gaussian curvature, that is H-2 = K, along the given curve. We express surfaces parametrically possessing the given curve and obtain conditions for the coefficient functions to satisfy H-2 = K along the curve. The theory is validated by illustrative examples..