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

Year 2023, Volume: 6 Issue: 3, 157 - 169, 30.09.2023

Büşra Sancı Fırat Yerlikaya

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.

Keywords

Helicoidal surface extrinsic curvature conformally flat pseudo-space conformally flat pseudo-metric

References

  • [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

Year 2023, Volume: 6 Issue: 3, 157 - 169, 30.09.2023

Büşra Sancı Fırat Yerlikaya

Abstract

References

  • [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
There are 8 citations in total.

Details

Primary Language English
Subjects Pure Mathematics (Other)
Journal Section Articles
Authors

Büşra Sancı 0000-0001-6815-889X

Fırat Yerlikaya 0000-0003-2360-1522

Publication Date September 30, 2023
Submission Date June 15, 2023
Acceptance Date September 13, 2023
Published in Issue Year 2023 Volume: 6 Issue: 3

Cite

APA Sancı, B., & Yerlikaya, F. (2023). Helicoidal Surfaces with Prescribed Curvatures in Some Conformally Flat Pseudo-Spaces of Dimensional Three. Fundamental Journal of Mathematics and Applications, 6(3), 157-169. https://doi.org/10.33401/fujma.1315178
AMA Sancı B, Yerlikaya F. Helicoidal Surfaces with Prescribed Curvatures in Some Conformally Flat Pseudo-Spaces of Dimensional Three. FUJMA. September 2023;6(3):157-169. doi:10.33401/fujma.1315178
Chicago Sancı, Büşra, and Fırat Yerlikaya. “Helicoidal Surfaces With Prescribed Curvatures in Some Conformally Flat Pseudo-Spaces of Dimensional Three”. Fundamental Journal of Mathematics and Applications 6, no. 3 (September 2023): 157-69. https://doi.org/10.33401/fujma.1315178.
EndNote Sancı B, Yerlikaya F (September 1, 2023) Helicoidal Surfaces with Prescribed Curvatures in Some Conformally Flat Pseudo-Spaces of Dimensional Three. Fundamental Journal of Mathematics and Applications 6 3 157–169.
IEEE B. Sancı and F. Yerlikaya, “Helicoidal Surfaces with Prescribed Curvatures in Some Conformally Flat Pseudo-Spaces of Dimensional Three”, FUJMA, vol. 6, no. 3, pp. 157–169, 2023, doi: 10.33401/fujma.1315178.
ISNAD Sancı, Büşra - Yerlikaya, Fırat. “Helicoidal Surfaces With Prescribed Curvatures in Some Conformally Flat Pseudo-Spaces of Dimensional Three”. Fundamental Journal of Mathematics and Applications 6/3 (September 2023), 157-169. https://doi.org/10.33401/fujma.1315178.
JAMA Sancı B, Yerlikaya F. Helicoidal Surfaces with Prescribed Curvatures in Some Conformally Flat Pseudo-Spaces of Dimensional Three. FUJMA. 2023;6:157–169.
MLA Sancı, Büşra and Fırat Yerlikaya. “Helicoidal Surfaces With Prescribed Curvatures in Some Conformally Flat Pseudo-Spaces of Dimensional Three”. Fundamental Journal of Mathematics and Applications, vol. 6, no. 3, 2023, pp. 157-69, doi:10.33401/fujma.1315178.
Vancouver Sancı B, Yerlikaya F. Helicoidal Surfaces with Prescribed Curvatures in Some Conformally Flat Pseudo-Spaces of Dimensional Three. FUJMA. 2023;6(3):157-69.
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