Research Article
BibTex RIS Cite

Non-null Surfaces with Constant Slope Ruling with Respect to Osculating Plane

Year 2020, , 240 - 255, 25.06.2020

Ayşe Yavuz , Fatma Ateş , Yusuf Yaylı

https://doi.org/10.37094/adyujsci.612485

Abstract

    The main purpose of this study is to investigate surface with a constant slope ruling with respect to osculating plane by using Frenet Frame according to casual characters in Minkowski space. In accordance with this purpose, surface with constant slope ruling with respect to osculating plane in Minkowski Space is defined and many features of this surface are investigated. In addition, examples of the given characterizations are obtained and the geometrical structures of these examples are be examined and visualized. 

Keywords

Ruled Surface Surface with Constant Slope Minkowski Space

References

  • [1] Erdoğdu M., Yavuz A., Some Characterizations for Involute-Evolute Curve Couples with Constant Curvatures in Minkowski Space, Afyon Kocatepe University Journal of Science and Engineering,. 19, 031303, 605-614, 2019.
  • [2] Erdoğdu, M., Parallel frame of non-lightlike curves in Minkowski space-time, International Journal of Geometric Methods in Modern Physics, 12, 16 pages, 2015.
  • [3] López, R., Differential geometry of curves and surfaces in Lorentz-Minkowski space. International Electronic Journal of Geometry, 7, 44-107, 2014.
  • [4] Kaya, F.E., Yavuz A., Harmonic curvatures of the strip in Minkowski space. Asian-European Journal of Mathematics, Vol. 11, No. 04, 1850061, 2018.
  • [5] Malecek K., Szarka J., Szarkova D., Surfaces with Constant Slope with Their Generalisation, The Journal of Polish Society for Geometry and Engineering Graphics, 19, 67-77, 2009.
  • [6] Walrave, J., Curves and Surfaces in Minkowski Space, Ph. D. thesis, K. U. Leuven, Fac. of Science Leuven, 1995.
  • [7] Önder, M., Uğurlu, H.H., Frenet Frames and Invariants of Timelike Ruled Surfaces, Ain Shams Engineering Journal, 4(3), 507-513, 2013.
  • [8] Wolfgang, K., Differential Geometry: Curves Surfaces Manifolds, ISBN-13: 978-0821839881, American Mathematical Society, 2002.
  • [9] Yaylı Y., Zıplar E., Ferret-Serret motion and ruled surfaces with constant slope, International Journal of the Physical Science, 6(29), 6727-6734, 2011.
  • [10] Do Carmo, M.P., Differential Geometry of Curves and Surfaces, Prentice Hall, ISBN New Jersy, 1976.

Year 2020, , 240 - 255, 25.06.2020

Ayşe Yavuz , Fatma Ateş , Yusuf Yaylı

https://doi.org/10.37094/adyujsci.612485

Abstract

References

  • [1] Erdoğdu M., Yavuz A., Some Characterizations for Involute-Evolute Curve Couples with Constant Curvatures in Minkowski Space, Afyon Kocatepe University Journal of Science and Engineering,. 19, 031303, 605-614, 2019.
  • [2] Erdoğdu, M., Parallel frame of non-lightlike curves in Minkowski space-time, International Journal of Geometric Methods in Modern Physics, 12, 16 pages, 2015.
  • [3] López, R., Differential geometry of curves and surfaces in Lorentz-Minkowski space. International Electronic Journal of Geometry, 7, 44-107, 2014.
  • [4] Kaya, F.E., Yavuz A., Harmonic curvatures of the strip in Minkowski space. Asian-European Journal of Mathematics, Vol. 11, No. 04, 1850061, 2018.
  • [5] Malecek K., Szarka J., Szarkova D., Surfaces with Constant Slope with Their Generalisation, The Journal of Polish Society for Geometry and Engineering Graphics, 19, 67-77, 2009.
  • [6] Walrave, J., Curves and Surfaces in Minkowski Space, Ph. D. thesis, K. U. Leuven, Fac. of Science Leuven, 1995.
  • [7] Önder, M., Uğurlu, H.H., Frenet Frames and Invariants of Timelike Ruled Surfaces, Ain Shams Engineering Journal, 4(3), 507-513, 2013.
  • [8] Wolfgang, K., Differential Geometry: Curves Surfaces Manifolds, ISBN-13: 978-0821839881, American Mathematical Society, 2002.
  • [9] Yaylı Y., Zıplar E., Ferret-Serret motion and ruled surfaces with constant slope, International Journal of the Physical Science, 6(29), 6727-6734, 2011.
  • [10] Do Carmo, M.P., Differential Geometry of Curves and Surfaces, Prentice Hall, ISBN New Jersy, 1976.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Ayşe Yavuz 0000-0002-0469-3786

Fatma Ateş 0000-0002-3529-1077

Yusuf Yaylı 0000-0003-4398-3855

Publication Date June 25, 2020
Submission Date August 28, 2019
Acceptance Date March 21, 2020
Published in Issue Year 2020

Cite

APA Yavuz, A., Ateş, F., & Yaylı, Y. (2020). Non-null Surfaces with Constant Slope Ruling with Respect to Osculating Plane. Adıyaman University Journal of Science, 10(1), 240-255. https://doi.org/10.37094/adyujsci.612485
AMA Yavuz A, Ateş F, Yaylı Y. Non-null Surfaces with Constant Slope Ruling with Respect to Osculating Plane. ADYU J SCI. June 2020;10(1):240-255. doi:10.37094/adyujsci.612485
Chicago Yavuz, Ayşe, Fatma Ateş, and Yusuf Yaylı. “Non-Null Surfaces With Constant Slope Ruling With Respect to Osculating Plane”. Adıyaman University Journal of Science 10, no. 1 (June 2020): 240-55. https://doi.org/10.37094/adyujsci.612485.
EndNote Yavuz A, Ateş F, Yaylı Y (June 1, 2020) Non-null Surfaces with Constant Slope Ruling with Respect to Osculating Plane. Adıyaman University Journal of Science 10 1 240–255.
IEEE A. Yavuz, F. Ateş, and Y. Yaylı, “Non-null Surfaces with Constant Slope Ruling with Respect to Osculating Plane”, ADYU J SCI, vol. 10, no. 1, pp. 240–255, 2020, doi: 10.37094/adyujsci.612485.
ISNAD Yavuz, Ayşe et al. “Non-Null Surfaces With Constant Slope Ruling With Respect to Osculating Plane”. Adıyaman University Journal of Science 10/1 (June 2020), 240-255. https://doi.org/10.37094/adyujsci.612485.
JAMA Yavuz A, Ateş F, Yaylı Y. Non-null Surfaces with Constant Slope Ruling with Respect to Osculating Plane. ADYU J SCI. 2020;10:240–255.
MLA Yavuz, Ayşe et al. “Non-Null Surfaces With Constant Slope Ruling With Respect to Osculating Plane”. Adıyaman University Journal of Science, vol. 10, no. 1, 2020, pp. 240-55, doi:10.37094/adyujsci.612485.
Vancouver Yavuz A, Ateş F, Yaylı Y. Non-null Surfaces with Constant Slope Ruling with Respect to Osculating Plane. ADYU J SCI. 2020;10(1):240-55.

...