Research Article
BibTex RIS Cite

A curve theory on sliced almost contact manifolds

Year 2022, Volume: 11 Issue: 1, 62 - 76, 30.04.2022
https://doi.org/10.54187/jnrs.1095343

Abstract

We have realized a gap between almost contact metric manifolds and contact metric manifolds in our studies. The examples that were given as Sasaki manifolds don't satisfy the condition of being contact metric manifold. As a result of our work, the sliced almost contact manifolds were formed and defined in \cite{MG}. In this paper we applied the theory of sliced almost contact manifolds to curves as a curve theory in three dimensional space. We define the $\pi-regular$ and $\pi-Legendre$ curves, also we give basic theorems on $\pi-Legendre$ curves and an example to $\pi-Legendre$ curves.

References

  • M. Gümüş, A new construction of Sasaki manifolds in semi-Riemann space and applications, PhD Dissertation, Çanakkale Onsekiz Mart University (2018) Çanakkale, Turkey (in Turkish).
  • C. Huygens, The pendulum clock or geometrical demonstrations concerning the motion of pendula as applied to clocks, Iowa State University Press, Iowa, 1986.
  • J. M. Child, The geometrical lectures of Isaac Barrow, The Open Court Publishing Company, 1916.
  • S. I. Newton, The mathematical principles of natural philosophy: Philosophiae naturalis principia mathematica, CreateSpace Independent Publishing Platform, 2016.
  • S. Lie, Verallgemeinerung und neue Verwertung der Jacobischen Multiplikatortheorie, Forhandlinger Christiania, (1874) 255-274.
  • J. Gray, Some global properties of contact structures, Annals of Mathematics, 69, (1959) 421-450.
  • J. W. Gibbs, A method of geometrical representation of the thermodynamic properties of substances by means of surfaces, Transactions of the Connecticut Academy of Arts and Sciences, 2, (1873) 382-404.
  • B. O'Neill, Semi-Riemannian geometry. with applications to relativity. Pure and Applied Mathematics, 103. Academic Press, Inc.[Harcourt Brace Jovanovich, Publishers], New York, 1983.
  • S. Sasaki, Y. Hatakeyama, On differentiable manifolds with contact metric structures, Journal of the Mathematical Society of Japan, 14, (1962) 249-271.
  • D. E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics, Springer-Verlag, 509, 1976.
  • C. Baikoussis, D. E. Blair, On Legendre curves in contact 3-manifolds, Geometriae Dedicata, 49, (1994) 135-142.
  • K. L. Duggal, A. Bejancu, Lightlike submanifolds of semi-Riemannian manifolds and applications, Kluwer Academic, 364, 1996.
  • M. Belkhelfa, I. E. Hiric, R. Rosca, L. Verstraelen, On Legendre curves in Riemannian and Lorentzian Sasaki spaces, Soochow Journal of Mathematics, 28, (2002) 81-91.
  • D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Progressin Mathematics 203. Birkhauser Boston, 2002.
  • Ç. Camcı, A curve theory in contact geometry, PhD Dissertation, Ankara University (2007) Ankara, Turkey (in Turkish).
  • K. L. Duggal, B. Şahin, Lightlike submanifolds of indefinite Sasakian manifolds, International Journal of Mathematics and Mathematical Sciences, 2007, (2007) Article ID: 057585.
  • M. Gümüş, Ç. Camcı, Riemannian curvature of a sliced contact metric manifold, Çanakkale Onsekiz Mart University, Journal of Graduate School of Natural and Applied Sciences, 4(2), (2018) 1-14.
  • K. Yano, M. Kon, Structures on manifolds, World Scientific, 1984.
  • Ç. Camcı, Extended cross product in 3-dimensional almost contact metric manifold with applications to curve theory, Turkish Journal of Mathematics, 36, (2012) 305-318.
Year 2022, Volume: 11 Issue: 1, 62 - 76, 30.04.2022
https://doi.org/10.54187/jnrs.1095343

Abstract

References

  • M. Gümüş, A new construction of Sasaki manifolds in semi-Riemann space and applications, PhD Dissertation, Çanakkale Onsekiz Mart University (2018) Çanakkale, Turkey (in Turkish).
  • C. Huygens, The pendulum clock or geometrical demonstrations concerning the motion of pendula as applied to clocks, Iowa State University Press, Iowa, 1986.
  • J. M. Child, The geometrical lectures of Isaac Barrow, The Open Court Publishing Company, 1916.
  • S. I. Newton, The mathematical principles of natural philosophy: Philosophiae naturalis principia mathematica, CreateSpace Independent Publishing Platform, 2016.
  • S. Lie, Verallgemeinerung und neue Verwertung der Jacobischen Multiplikatortheorie, Forhandlinger Christiania, (1874) 255-274.
  • J. Gray, Some global properties of contact structures, Annals of Mathematics, 69, (1959) 421-450.
  • J. W. Gibbs, A method of geometrical representation of the thermodynamic properties of substances by means of surfaces, Transactions of the Connecticut Academy of Arts and Sciences, 2, (1873) 382-404.
  • B. O'Neill, Semi-Riemannian geometry. with applications to relativity. Pure and Applied Mathematics, 103. Academic Press, Inc.[Harcourt Brace Jovanovich, Publishers], New York, 1983.
  • S. Sasaki, Y. Hatakeyama, On differentiable manifolds with contact metric structures, Journal of the Mathematical Society of Japan, 14, (1962) 249-271.
  • D. E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics, Springer-Verlag, 509, 1976.
  • C. Baikoussis, D. E. Blair, On Legendre curves in contact 3-manifolds, Geometriae Dedicata, 49, (1994) 135-142.
  • K. L. Duggal, A. Bejancu, Lightlike submanifolds of semi-Riemannian manifolds and applications, Kluwer Academic, 364, 1996.
  • M. Belkhelfa, I. E. Hiric, R. Rosca, L. Verstraelen, On Legendre curves in Riemannian and Lorentzian Sasaki spaces, Soochow Journal of Mathematics, 28, (2002) 81-91.
  • D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Progressin Mathematics 203. Birkhauser Boston, 2002.
  • Ç. Camcı, A curve theory in contact geometry, PhD Dissertation, Ankara University (2007) Ankara, Turkey (in Turkish).
  • K. L. Duggal, B. Şahin, Lightlike submanifolds of indefinite Sasakian manifolds, International Journal of Mathematics and Mathematical Sciences, 2007, (2007) Article ID: 057585.
  • M. Gümüş, Ç. Camcı, Riemannian curvature of a sliced contact metric manifold, Çanakkale Onsekiz Mart University, Journal of Graduate School of Natural and Applied Sciences, 4(2), (2018) 1-14.
  • K. Yano, M. Kon, Structures on manifolds, World Scientific, 1984.
  • Ç. Camcı, Extended cross product in 3-dimensional almost contact metric manifold with applications to curve theory, Turkish Journal of Mathematics, 36, (2012) 305-318.
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Mehmet Gümüş 0000-0001-7938-2918

Çetin Camcı 0000-0002-0122-559X

Early Pub Date April 30, 2022
Publication Date April 30, 2022
Published in Issue Year 2022 Volume: 11 Issue: 1

Cite

APA Gümüş, M., & Camcı, Ç. (2022). A curve theory on sliced almost contact manifolds. Journal of New Results in Science, 11(1), 62-76. https://doi.org/10.54187/jnrs.1095343
AMA Gümüş M, Camcı Ç. A curve theory on sliced almost contact manifolds. JNRS. April 2022;11(1):62-76. doi:10.54187/jnrs.1095343
Chicago Gümüş, Mehmet, and Çetin Camcı. “A Curve Theory on Sliced Almost Contact Manifolds”. Journal of New Results in Science 11, no. 1 (April 2022): 62-76. https://doi.org/10.54187/jnrs.1095343.
EndNote Gümüş M, Camcı Ç (April 1, 2022) A curve theory on sliced almost contact manifolds. Journal of New Results in Science 11 1 62–76.
IEEE M. Gümüş and Ç. Camcı, “A curve theory on sliced almost contact manifolds”, JNRS, vol. 11, no. 1, pp. 62–76, 2022, doi: 10.54187/jnrs.1095343.
ISNAD Gümüş, Mehmet - Camcı, Çetin. “A Curve Theory on Sliced Almost Contact Manifolds”. Journal of New Results in Science 11/1 (April 2022), 62-76. https://doi.org/10.54187/jnrs.1095343.
JAMA Gümüş M, Camcı Ç. A curve theory on sliced almost contact manifolds. JNRS. 2022;11:62–76.
MLA Gümüş, Mehmet and Çetin Camcı. “A Curve Theory on Sliced Almost Contact Manifolds”. Journal of New Results in Science, vol. 11, no. 1, 2022, pp. 62-76, doi:10.54187/jnrs.1095343.
Vancouver Gümüş M, Camcı Ç. A curve theory on sliced almost contact manifolds. JNRS. 2022;11(1):62-76.


TR Dizin 31688

EBSCO30456


Electronic Journals Library EZB   30356

 DOAJ   30355                                             

WorldCat  30357                                             303573035530355

Academindex   30358

SOBİAD   30359

Scilit   30360


29388 As of 2021, JNRS is licensed under a Creative Commons Attribution-NonCommercial 4.0 International Licence (CC BY-NC).