Helicoidal surfaces in some conformally flat pseudo-spaces of dimensional three

Yerlikaya F.

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, cilt.20, sa.03, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 20 Sayı: 03
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1142/s0219887823500524
  • Dergi Adı: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Conformally flat pseudo-space, helicoidal surface, extrinsic curvature, conformally flat pseudo-metric, MINKOWSKI SPACE, CURVATURE
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

We introduce the complete pseudo-Riemannian manifold E-3(1) with a conformally flat pseudo-metric satisfying Einstein's equation. First, we get a theorem that associates the curvatures of a non- degenerate surface belonging to conformally equivalent spaces, say E-3(1) and R-1(3). Next, we evaluate the existence of non-degenerate helicoidal surfaces in some conformally flat pseudo-spaces with pseudo-metrics corresponding to particular conformal factors (for example, a certain rotational symmetry with translational symmetry). We determine these conformal factors according to the causal characters of the axis of rotation. Right after, we get a two-parameter family of non-degenerate helicoidal surfaces with prescribed extrinsic curvature or mean curvature given by smooth functions, corresponding to both spacelike and timelike axes of rotation. As for the lightlike axis, we discuss some particular cases.