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Year 2020, Volume: 3 Issue: 1, 17 - 24, 10.06.2020

Emre Öztürk

https://doi.org/10.33401/fujma.643374

Abstract

References

  • N. Kerzman, E.M. Stein, The Cauchy Kernel, the Szeg¨o Kernel, and the Riemann Mapping Function, Math.Ann. 236 (1978), 85-93.
  • H.P. Boas, A Geometric Characterization of the Ball and the Bochner-Martinelli Kernel, Math. Ann. 248 (1980), 275-278.
  • H.P. Boas, Spheres and Cylinders: A Local Geometric Characterization, Illinois Journal of Mathematics, 28(1) (1984), 120-124.
  • B. Wegner, A Differential Geometric Proof of the Local Geometric Characterization of Spheres and Cylinders by Boas, Mathematica Balkanica 2 (1988),294-295.
  • D.S. Kim, Y.H. Kim, New Characterizations of Spheres, Cylinders and W−Curves, Linear Algebra and Its Applications 432 (2010), 3002-3006.
  • Y. H. Kim, K. E. Lee, Surfaces of Euclidean 4-Space Whose Geodesics are W-Curves, Nihonkai Math. J., 4 (1993), 221-232.
  • B. O’Neill, Semi-Riemann Geometry with Applications to Relativity, Academic Press. Inc., (1983).
  • E. Öztürk, Y. Yaylı, W-Curves In Lorentz-Minkowski Space, Mathematical Sciences and Applications E-Notes, 5(2) (2017), 76-88.
  • C. Ekici, E. Ozüsağlam, M. Çimdiker, E. Öztürk, On The Curvatures of Viviani Ruled Surface, Ciencia e Tecnica Vitivinicola, 29(7) (2014), 449-475

Gauss Map and Local Approach of Isoparametric Surfaces in Lorentz and Euclidean Space

Year 2020, Volume: 3 Issue: 1, 17 - 24, 10.06.2020

Emre Öztürk

https://doi.org/10.33401/fujma.643374

Abstract

In this study, we determine the isoparametric surfaces and we give the Gauss map of these surfaces by semi symmetric matrix, in Lorentz space. Also we define any chord property and we show that the surfaces which have the chord property corresponds to isoparametric surfaces. Moreover, we consider the chord property locally and we give some examples in the Euclidean space.

Keywords

Gauss map Isoparametric surface Linear operator

References

  • N. Kerzman, E.M. Stein, The Cauchy Kernel, the Szeg¨o Kernel, and the Riemann Mapping Function, Math.Ann. 236 (1978), 85-93.
  • H.P. Boas, A Geometric Characterization of the Ball and the Bochner-Martinelli Kernel, Math. Ann. 248 (1980), 275-278.
  • H.P. Boas, Spheres and Cylinders: A Local Geometric Characterization, Illinois Journal of Mathematics, 28(1) (1984), 120-124.
  • B. Wegner, A Differential Geometric Proof of the Local Geometric Characterization of Spheres and Cylinders by Boas, Mathematica Balkanica 2 (1988),294-295.
  • D.S. Kim, Y.H. Kim, New Characterizations of Spheres, Cylinders and W−Curves, Linear Algebra and Its Applications 432 (2010), 3002-3006.
  • Y. H. Kim, K. E. Lee, Surfaces of Euclidean 4-Space Whose Geodesics are W-Curves, Nihonkai Math. J., 4 (1993), 221-232.
  • B. O’Neill, Semi-Riemann Geometry with Applications to Relativity, Academic Press. Inc., (1983).
  • E. Öztürk, Y. Yaylı, W-Curves In Lorentz-Minkowski Space, Mathematical Sciences and Applications E-Notes, 5(2) (2017), 76-88.
  • C. Ekici, E. Ozüsağlam, M. Çimdiker, E. Öztürk, On The Curvatures of Viviani Ruled Surface, Ciencia e Tecnica Vitivinicola, 29(7) (2014), 449-475
There are 9 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Emre Öztürk 0000-0001-6638-3233

Submission Date January 5, 2019
Acceptance Date January 23, 2020
Publication Date June 10, 2020
Published in Issue Year 2020 Volume: 3 Issue: 1

Cite

APA Öztürk, E. (2020). Gauss Map and Local Approach of Isoparametric Surfaces in Lorentz and Euclidean Space. Fundamental Journal of Mathematics and Applications, 3(1), 17-24. https://doi.org/10.33401/fujma.643374
AMA Öztürk E. Gauss Map and Local Approach of Isoparametric Surfaces in Lorentz and Euclidean Space. Fundam. J. Math. Appl. June 2020;3(1):17-24. doi:10.33401/fujma.643374
Chicago Öztürk, Emre. “Gauss Map and Local Approach of Isoparametric Surfaces in Lorentz and Euclidean Space”. Fundamental Journal of Mathematics and Applications 3, no. 1 (June 2020): 17-24. https://doi.org/10.33401/fujma.643374.
EndNote Öztürk E (June 1, 2020) Gauss Map and Local Approach of Isoparametric Surfaces in Lorentz and Euclidean Space. Fundamental Journal of Mathematics and Applications 3 1 17–24.
IEEE E. Öztürk, “Gauss Map and Local Approach of Isoparametric Surfaces in Lorentz and Euclidean Space”, Fundam. J. Math. Appl., vol. 3, no. 1, pp. 17–24, 2020, doi: 10.33401/fujma.643374.
ISNAD Öztürk, Emre. “Gauss Map and Local Approach of Isoparametric Surfaces in Lorentz and Euclidean Space”. Fundamental Journal of Mathematics and Applications 3/1 (June2020), 17-24. https://doi.org/10.33401/fujma.643374.
JAMA Öztürk E. Gauss Map and Local Approach of Isoparametric Surfaces in Lorentz and Euclidean Space. Fundam. J. Math. Appl. 2020;3:17–24.
MLA Öztürk, Emre. “Gauss Map and Local Approach of Isoparametric Surfaces in Lorentz and Euclidean Space”. Fundamental Journal of Mathematics and Applications, vol. 3, no. 1, 2020, pp. 17-24, doi:10.33401/fujma.643374.
Vancouver Öztürk E. Gauss Map and Local Approach of Isoparametric Surfaces in Lorentz and Euclidean Space. Fundam. J. Math. Appl. 2020;3(1):17-24.

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