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Some Theorems on Timelike Ruled Surfaces

Year 2019, Volume: 14 Issue: 2, 49 - 57, 27.09.2019

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

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 TJST
Authors

Mehmet Önder 0000-0002-9354-5530

Publication Date September 27, 2019
Submission Date October 30, 2017
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.
AMA Önder M. Some Theorems on Timelike Ruled Surfaces. TJST. September 2019;14(2):49-57.
Chicago Önder, Mehmet. “Some Theorems on Timelike Ruled Surfaces”. Turkish Journal of Science and Technology 14, no. 2 (September 2019): 49-57.
EndNote Önder M (September 1, 2019) Some Theorems on Timelike Ruled Surfaces. Turkish Journal of Science and Technology 14 2 49–57.
IEEE M. Önder, “Some Theorems on Timelike Ruled Surfaces”, TJST, vol. 14, no. 2, pp. 49–57, 2019.
ISNAD Önder, Mehmet. “Some Theorems on Timelike Ruled Surfaces”. Turkish Journal of Science and Technology 14/2 (September 2019), 49-57.
JAMA 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, 2019, pp. 49-57.
Vancouver Önder M. Some Theorems on Timelike Ruled Surfaces. TJST. 2019;14(2):49-57.