General rotational xi-surfaces in Euclidean spaces

Arslan K., Aydin Y., Bulca B.

TURKISH JOURNAL OF MATHEMATICS, vol.45, no.3, pp.1287-1299, 2021 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.3906/mat-2006-93
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1287-1299
  • Bursa Uludag University Affiliated: Yes

Abstract

The general rotational surfaces in the Euclidean 4-space R-4 was first studied by Moore (1919). The Vranceanu surfaces are the special examples of these kind of surfaces. Self-shrinker flows arise as special solution of the mean curvature flow that preserves the shape of the evolving submanifold. In addition, xi-surfaces are the generalization of self-shrinker surfaces. In the present article we consider xi-surfaces in Euclidean spaces. We obtained some results related with rotational surfaces in Euclidean xi- space R-4 to become self-shrinkers. Furthermore, we classify the general rotational xi-surfaces with constant mean curvature. As an application, we give some examples of self-shrinkers and rotational xi-surfaces in R-4.