Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2018, , 1760 - 1764, 01.12.2018
https://doi.org/10.16984/saufenbilder.409153

Öz

Kaynakça

  • V. Asil, T. Körpinar, and E. Turhan. "On inextensible flows of tangent developable of biharmonic B-Slant helices according to Bishop frames in the special 3-dimensional Kenmotsu manifold." Boletim da Sociedade Paranaense de Matemática, vol. 31, no. 1, pp. 89-97, 2013.J. E. Brosius, “Rank 2-Vector Bundels on a Ruled Surface,” Math. Ann., vol. 256, pp. 155-168, 1983.M. P. Do Carmo, “Differential Geometry of Curves and Surfaces, Englewood Cliffs,” Prentice Hall, 1976.G. Elber and K. Myung-Soo, “The Bisector Surface of Rational Space Curves,” ACM Transactions on Grap., vol. 17, pp. 32-49 1998.G. Elber and M. S. Kim, “A Computational Model for Nonrational Bisector Surfaces: Curve-Surface and Surface-Surface Bisectors,” pp. 364-372, 2000.A. G. Horvath, “Bisectors in Minkowski 3-space,” Sci.Reseach J.Bolyai, 2000.W. Kühnel, “Curves- Surfaces- Manifolds, Differantial Geometry,” Amer. Math. Soc., 2003.C. Li, R. Wang and C. Zhu, “An Approach For Designing a Developable Surface Through a Given Line of Curvature,” Comp. Aid. Des., vol. 45, pp. 621-627, 2013.B. O'Neill, “Elementary Differential Geometry,” New York, Academic Press Inc., 1966.M. Önder and H. H. Uğurlu, “Mannheim Offsets of the Timelike Ruled Surfaces with Spacelike Rulings in Dual Lorentzian Space,” arXiv:0906.4660v3 [math.Dg]M. Peternell, “Geometric Properties of Bisector Surfaces,” Graphical Models, vol. 62 pp. 202-236, 2000.M. T. Sariaydin and V. Asil, “On Bisector Surface in Minkowski Space,” Prespacetime, vol. 8, no. 7, pp. 865-874, 2017.T. Körpınar and E. Turhan, "Time-tangent surfaces around Biharmonic particles and its Lorentz transformations in Heisenberg spacetime." International Journal of Theoretical Physics, vol. 52, no. 12 pp. 4427-4438, 2013.T. Körpınar, and E. Turhan, "Rectifying Developable Surface of Timelike Biharmonic Curve In The Lorentzian Heisenberg Group Heis." TWMS Journal of Applied and Engineering Mathematics, vol. 2, no. 1, pp, 101, 2012.T. Körpınar, and E. Turhan, "New solution of differential equation for dual curvatures of dual spacelike biharmonic curves with timelike principal normal according to dual Bishop frames in the dual Lorentzian space." Acta Universitatis Apulensis, vol. 30, pp. 77-86, 2012.T. Körpınar, and E. Turhan, "Parallel Surfaces to S-Tangent Surfaces of Biharmonic S-Curves according to Sabban Frame in Heisenberg Group Heis3." Journal of Science and Arts vol. 2, no. 20, pp. 229-236, 2012.Y. Ünlütürk and E. Ozusaglam, "On parallel surfaces in Minkowski 3-space." TWMS Journal of Applied and Engineering Mathematics, vol. 3, no. 2, pp. 214, 2013.Y. Ünlütürk and C. Ekici, "Parallel Surfaces of Spacelike Ruled Weingarten Surfaces in." New Trends in Mathematical Sciences, vol. 1, no. 1, pp. 85-92, 2015.Y. Ünlütürk, "On Timelike Parallel Ruled Surfaces With Spacelike Ruling." Konuralp Jornal of Mathematics (KJM), vol. 1, no. 1, 24-33, 2013.Y. Ünlütürk, M. Cimdiker, and C. Ekici, "Characteristic properties of the parallel ruled surfaces with Darboux frame in Euclidean 3-space." Communication in Mathematical Modeling and Applications, vol. 1, no. 1, pp. 26-43, 2016.

Bisector Surfaces Through A Common Line of Curvatures and Its Classifications

Yıl 2018, , 1760 - 1764, 01.12.2018
https://doi.org/10.16984/saufenbilder.409153

Öz

In this paper, we study the Bisector surface, which defines
the line of curvature on a surface play an importance role. Firstly, the
Bisector surface constructed by a point and a space curve given in Euclidean
3-space. Then, it is investigated that the necessary and sufficient condition
for directrix curve of this surface to satisfy line of curvature. After this,
we classify the Bisector surfaces.

Kaynakça

  • V. Asil, T. Körpinar, and E. Turhan. "On inextensible flows of tangent developable of biharmonic B-Slant helices according to Bishop frames in the special 3-dimensional Kenmotsu manifold." Boletim da Sociedade Paranaense de Matemática, vol. 31, no. 1, pp. 89-97, 2013.J. E. Brosius, “Rank 2-Vector Bundels on a Ruled Surface,” Math. Ann., vol. 256, pp. 155-168, 1983.M. P. Do Carmo, “Differential Geometry of Curves and Surfaces, Englewood Cliffs,” Prentice Hall, 1976.G. Elber and K. Myung-Soo, “The Bisector Surface of Rational Space Curves,” ACM Transactions on Grap., vol. 17, pp. 32-49 1998.G. Elber and M. S. Kim, “A Computational Model for Nonrational Bisector Surfaces: Curve-Surface and Surface-Surface Bisectors,” pp. 364-372, 2000.A. G. Horvath, “Bisectors in Minkowski 3-space,” Sci.Reseach J.Bolyai, 2000.W. Kühnel, “Curves- Surfaces- Manifolds, Differantial Geometry,” Amer. Math. Soc., 2003.C. Li, R. Wang and C. Zhu, “An Approach For Designing a Developable Surface Through a Given Line of Curvature,” Comp. Aid. Des., vol. 45, pp. 621-627, 2013.B. O'Neill, “Elementary Differential Geometry,” New York, Academic Press Inc., 1966.M. Önder and H. H. Uğurlu, “Mannheim Offsets of the Timelike Ruled Surfaces with Spacelike Rulings in Dual Lorentzian Space,” arXiv:0906.4660v3 [math.Dg]M. Peternell, “Geometric Properties of Bisector Surfaces,” Graphical Models, vol. 62 pp. 202-236, 2000.M. T. Sariaydin and V. Asil, “On Bisector Surface in Minkowski Space,” Prespacetime, vol. 8, no. 7, pp. 865-874, 2017.T. Körpınar and E. Turhan, "Time-tangent surfaces around Biharmonic particles and its Lorentz transformations in Heisenberg spacetime." International Journal of Theoretical Physics, vol. 52, no. 12 pp. 4427-4438, 2013.T. Körpınar, and E. Turhan, "Rectifying Developable Surface of Timelike Biharmonic Curve In The Lorentzian Heisenberg Group Heis." TWMS Journal of Applied and Engineering Mathematics, vol. 2, no. 1, pp, 101, 2012.T. Körpınar, and E. Turhan, "New solution of differential equation for dual curvatures of dual spacelike biharmonic curves with timelike principal normal according to dual Bishop frames in the dual Lorentzian space." Acta Universitatis Apulensis, vol. 30, pp. 77-86, 2012.T. Körpınar, and E. Turhan, "Parallel Surfaces to S-Tangent Surfaces of Biharmonic S-Curves according to Sabban Frame in Heisenberg Group Heis3." Journal of Science and Arts vol. 2, no. 20, pp. 229-236, 2012.Y. Ünlütürk and E. Ozusaglam, "On parallel surfaces in Minkowski 3-space." TWMS Journal of Applied and Engineering Mathematics, vol. 3, no. 2, pp. 214, 2013.Y. Ünlütürk and C. Ekici, "Parallel Surfaces of Spacelike Ruled Weingarten Surfaces in." New Trends in Mathematical Sciences, vol. 1, no. 1, pp. 85-92, 2015.Y. Ünlütürk, "On Timelike Parallel Ruled Surfaces With Spacelike Ruling." Konuralp Jornal of Mathematics (KJM), vol. 1, no. 1, 24-33, 2013.Y. Ünlütürk, M. Cimdiker, and C. Ekici, "Characteristic properties of the parallel ruled surfaces with Darboux frame in Euclidean 3-space." Communication in Mathematical Modeling and Applications, vol. 1, no. 1, pp. 26-43, 2016.
Toplam 1 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Muhammed Talat Sarıaydın 0000-0002-3613-4276

Yayımlanma Tarihi 1 Aralık 2018
Gönderilme Tarihi 23 Mart 2018
Kabul Tarihi 29 Mayıs 2018
Yayımlandığı Sayı Yıl 2018

Kaynak Göster

APA Sarıaydın, M. T. (2018). Bisector Surfaces Through A Common Line of Curvatures and Its Classifications. Sakarya University Journal of Science, 22(6), 1760-1764. https://doi.org/10.16984/saufenbilder.409153
AMA Sarıaydın MT. Bisector Surfaces Through A Common Line of Curvatures and Its Classifications. SAUJS. Aralık 2018;22(6):1760-1764. doi:10.16984/saufenbilder.409153
Chicago Sarıaydın, Muhammed Talat. “Bisector Surfaces Through A Common Line of Curvatures and Its Classifications”. Sakarya University Journal of Science 22, sy. 6 (Aralık 2018): 1760-64. https://doi.org/10.16984/saufenbilder.409153.
EndNote Sarıaydın MT (01 Aralık 2018) Bisector Surfaces Through A Common Line of Curvatures and Its Classifications. Sakarya University Journal of Science 22 6 1760–1764.
IEEE M. T. Sarıaydın, “Bisector Surfaces Through A Common Line of Curvatures and Its Classifications”, SAUJS, c. 22, sy. 6, ss. 1760–1764, 2018, doi: 10.16984/saufenbilder.409153.
ISNAD Sarıaydın, Muhammed Talat. “Bisector Surfaces Through A Common Line of Curvatures and Its Classifications”. Sakarya University Journal of Science 22/6 (Aralık 2018), 1760-1764. https://doi.org/10.16984/saufenbilder.409153.
JAMA Sarıaydın MT. Bisector Surfaces Through A Common Line of Curvatures and Its Classifications. SAUJS. 2018;22:1760–1764.
MLA Sarıaydın, Muhammed Talat. “Bisector Surfaces Through A Common Line of Curvatures and Its Classifications”. Sakarya University Journal of Science, c. 22, sy. 6, 2018, ss. 1760-4, doi:10.16984/saufenbilder.409153.
Vancouver Sarıaydın MT. Bisector Surfaces Through A Common Line of Curvatures and Its Classifications. SAUJS. 2018;22(6):1760-4.

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