KaydedilenlerDerginizi ekleyin

Dergiler / Fundamental Journal of Mathematics and Applications / 2023 / Cilt: 6 Sayı: 3

Helicoidal Surfaces with Prescribed Curvatures in Some Conformally Flat Pseudo-Spaces of Dimensional Three

Büşra SANCI
Fırat YERLİKAYA
Sayfa
157–169
Yayın Tarihi
2023-09-30
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Also, we support them with examples.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this work, we consider the problem of finding explicit parametrizations for non-degenerate helicoidal surfaces with prescribed curvatures in some conformally flat pseudo-spaces with conformal pseudo-metrics whose conformal factors are related to three types of generic cylindrical functions.
📊
Temel Bulgular & Veri:In the first two, we get a two-parameter family of these surfaces with prescribed extrinsic curvature or mean curvature given by smooth functions.
💡
Sonuç & Katkı:Also, we support them with examples.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Helicoidal surface · extrinsic curvature · conformally flat pseudo-space

Abstract

In this work, we consider the problem of finding explicit parametrizations for non-degenerate helicoidal surfaces with prescribed curvatures in some conformally flat pseudo-spaces with conformal pseudo-metrics whose conformal factors are related to three types of generic cylindrical functions. In the first two, we get a two-parameter family of these surfaces with prescribed extrinsic curvature or mean curvature given by smooth functions. In the last one, we discover a one-parameter family when both curvatures of these surfaces are zero; however, we find a two-parameter family when either one of those curvatures is zero. Also, we support them with examples.

🔖

Bu Makaleye Atıf Yap

SANCI, B., YERLİKAYA, F. (2023). Helicoidal Surfaces with Prescribed Curvatures in Some Conformally Flat Pseudo-Spaces of Dimensional Three. Fundamental Journal of Mathematics and Applications, Cilt: 6 Sayı: 3, 157–169. https://ajindex.com/articles/964188

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (8)

  1. A. V. Corro, R. Pina, M. A. Souza, Surfaces of rotation with constant extrinsic curvature in a conformally flat 3-space, Results Math., 60 (2011), 225–234
  2. A. V. Corro, M. A. Souza, R. Pina, Classes of Weingarten surfaces in S2 R, Houston J. Math., 46 (2020), 651-654
  3. B. P. Lima, P. A. Souza, B. M. Vieira, Helicoidal hypersurfaces and graphs in conformally flat spaces, Results Math., 77 (2022), 1-16
  4. K. O. Araujo, N. Cui, R. S. Pina, Helicoidal minimal surfaces in a conformally flat 3-space, Bull. Korean Math., 53(2) (2016), 531-540
  5. K. O. Araujo, A. V. Corro, R. S. Pina, M. A. Souza, Complete surfaces with zero curvatures in conformally flat spaces, Publ. Math. Debrecen., 96(3-4) (2020), 363-376
  6. C. W. Lee, J. W. Lee, D. W. Yoon, On helicoidal surfaces in a conformally flat 3-space, Mediterr. J. Math., 14 (2017), 1-9
  7. C. W. Lee, J. W. Lee, D. W. Yoon, Helicoidal surfaces with prescribed curvatures in a conformally flat 3-space, Georgian Math. J., 28(5) (2021), 755-763
  8. F. Yerlikaya, Helicoidal surfaces in some conformally flat pseudo-spaces of dimensional three, Int. J. Geom. Methods Mod., 20(3) (2023), 2350052-76