Research Article
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Some Theorems on Timelike Ruled Surfaces

Year 2019, Volume: 14 Issue: 2, 49 - 57, 27.09.2019
https://izlik.org/JA93BN74FL

Abstract

In this study, we investigate the existence
theorems for timelike ruled surfaces in Minkowski 3-space . We obtain a general system and give the existence theorems
for a timelike ruled surface according to Gaussian curvature, distribution
parameter and strictional distance. Moreover, we give some special cases such
as the directirx of the surface is a geodesic, an asymptotic line, a line of
curvature or a general helix.

References

  • [1] Guggenheimer H. Differential Geometry. London. McGraw-Hill Book Comp. Inc. Lib. Cong. Cat. Card No. 68-12118, 1963.[2] Karger A, Novak J. Space Kinematics and Lie Groups. Prague Czechoslovakia: STNL Publishers of Technical Lit 1978.[3] Ravani B, Ku TS. Bertrand Offsets of ruled and developable surfaces. Comp Aided Geom Design 1991; 2(23): 145-152. [4] Abdel-All NH, Abdel-Baky RA, Hamdoon FM. Ruled surfaces with timelike rulings. App. Math. and Comp 2004; 147: 241-253. [5] Küçük A. On the developable timelike trajectory ruled surfaces in Lorentz 3-space . App Math and Comp 2004; 157: 483-489.[6] Önder M, Uğurlu HH. Frenet frames and invariants of timelike ruled surfaces. Ain Shams Eng J 2013; 4: 507-513.[7] Blaschke W, Leichtweiss K. Elementare Differentialgeometrie. Springer, 1973.[8] Do Carmo M. Differential geometry of curves and surfaces. New Jersey. Prentice-Hall, 1976.[9] Struik DJ. Lectures on classical differential geometry. New York. Dover Publications, Inc. 1988.[10] Kamenarovic I. Existence Theorems for Ruled Surfaces in the Galilean Space . Rad Hrvatske Akad. Znan. Umj. Mat 1991; 10(456): 183-186.[11] O’Neill B. Semi-Riemannian Geometry with Applications to Relativity. London. Academic Press, 1983.[12] Uğurlu HH, Çalışkan A. Darboux Ani Dönme Vektörleri ile Spacelike ve Timelike Yüzeyler Geometrisi. Manisa. Celal Bayar Üniversitesi Yayınları. Yayın No: 0006, 2012.[13] Walrave J. Curves and Surfaces in Minkowski space. PhD. thesis, K.U. Leuven: Fac. of Science, Leuven, 1995.[14] Ratcliffe JG. Foundations of Hyperbolic Manifolds. Springer, 2006. [15] Kazaz M, Özdemir A, Güroğlu T. On the determination of a developable timelike ruled surface. SDÜ Fen-Edebiyat Fakültesi Fen Dergisi (E-Dergi) 2008; 3(1): 72-79.

Year 2019, Volume: 14 Issue: 2, 49 - 57, 27.09.2019
https://izlik.org/JA93BN74FL

Abstract

References

  • [1] Guggenheimer H. Differential Geometry. London. McGraw-Hill Book Comp. Inc. Lib. Cong. Cat. Card No. 68-12118, 1963.[2] Karger A, Novak J. Space Kinematics and Lie Groups. Prague Czechoslovakia: STNL Publishers of Technical Lit 1978.[3] Ravani B, Ku TS. Bertrand Offsets of ruled and developable surfaces. Comp Aided Geom Design 1991; 2(23): 145-152. [4] Abdel-All NH, Abdel-Baky RA, Hamdoon FM. Ruled surfaces with timelike rulings. App. Math. and Comp 2004; 147: 241-253. [5] Küçük A. On the developable timelike trajectory ruled surfaces in Lorentz 3-space . App Math and Comp 2004; 157: 483-489.[6] Önder M, Uğurlu HH. Frenet frames and invariants of timelike ruled surfaces. Ain Shams Eng J 2013; 4: 507-513.[7] Blaschke W, Leichtweiss K. Elementare Differentialgeometrie. Springer, 1973.[8] Do Carmo M. Differential geometry of curves and surfaces. New Jersey. Prentice-Hall, 1976.[9] Struik DJ. Lectures on classical differential geometry. New York. Dover Publications, Inc. 1988.[10] Kamenarovic I. Existence Theorems for Ruled Surfaces in the Galilean Space . Rad Hrvatske Akad. Znan. Umj. Mat 1991; 10(456): 183-186.[11] O’Neill B. Semi-Riemannian Geometry with Applications to Relativity. London. Academic Press, 1983.[12] Uğurlu HH, Çalışkan A. Darboux Ani Dönme Vektörleri ile Spacelike ve Timelike Yüzeyler Geometrisi. Manisa. Celal Bayar Üniversitesi Yayınları. Yayın No: 0006, 2012.[13] Walrave J. Curves and Surfaces in Minkowski space. PhD. thesis, K.U. Leuven: Fac. of Science, Leuven, 1995.[14] Ratcliffe JG. Foundations of Hyperbolic Manifolds. Springer, 2006. [15] Kazaz M, Özdemir A, Güroğlu T. On the determination of a developable timelike ruled surface. SDÜ Fen-Edebiyat Fakültesi Fen Dergisi (E-Dergi) 2008; 3(1): 72-79.
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Details

Primary Language English
Journal Section Research Article
Authors

Mehmet Önder 0000-0002-9354-5530

Submission Date October 30, 2017
Publication Date September 27, 2019
IZ https://izlik.org/JA93BN74FL
Published in Issue Year 2019 Volume: 14 Issue: 2

Cite

APA Önder, M. (2019). Some Theorems on Timelike Ruled Surfaces. Turkish Journal of Science and Technology, 14(2), 49-57. https://izlik.org/JA93BN74FL
AMA 1.Önder M. Some Theorems on Timelike Ruled Surfaces. TJST. 2019;14(2):49-57. https://izlik.org/JA93BN74FL
Chicago Önder, Mehmet. 2019. “Some Theorems on Timelike Ruled Surfaces”. Turkish Journal of Science and Technology 14 (2): 49-57. https://izlik.org/JA93BN74FL.
EndNote Önder M (September 1, 2019) Some Theorems on Timelike Ruled Surfaces. Turkish Journal of Science and Technology 14 2 49–57.
IEEE [1]M. Önder, “Some Theorems on Timelike Ruled Surfaces”, TJST, vol. 14, no. 2, pp. 49–57, Sept. 2019, [Online]. Available: https://izlik.org/JA93BN74FL
ISNAD Önder, Mehmet. “Some Theorems on Timelike Ruled Surfaces”. Turkish Journal of Science and Technology 14/2 (September 1, 2019): 49-57. https://izlik.org/JA93BN74FL.
JAMA 1.Önder M. Some Theorems on Timelike Ruled Surfaces. TJST. 2019;14:49–57.
MLA Önder, Mehmet. “Some Theorems on Timelike Ruled Surfaces”. Turkish Journal of Science and Technology, vol. 14, no. 2, Sept. 2019, pp. 49-57, https://izlik.org/JA93BN74FL.
Vancouver 1.Mehmet Önder. Some Theorems on Timelike Ruled Surfaces. TJST [Internet]. 2019 Sep. 1;14(2):49-57. Available from: https://izlik.org/JA93BN74FL