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A NOTE ON KENMOTSU MANIFOLDS ADMITTING GENERALIZED TANAKA-WEBSTER CONNECTION

Year 2022, , 122 - 128, 31.07.2022
https://doi.org/10.33773/jum.1134765

Abstract

In the present paper, we investigate some tensor conditions of Kenmotsu manifolds with the generalized Tanaka-Webster connection. Using
the Q tensor whose trace is the well-known Z-tensor, we prove the conditions ξ − Q∗ flat, ϕ − Q∗ flat Kenmotsu manifold with respect to the generalized Tanaka-Webster connection.

References

  • [1] C.A. Mantica, Y.J. Suh, Pseudo Q−symmetric Riemannian manifolds. Int. J. Geom. Methods Mod. Phys. vol.10, pp.1-25, (2013).
  • [2] C.A. Mantica, L.G. Molinari, Riemann compatible tensors. Colloq. Math.vol.128 No.2, pp.197-200, (2012).
  • [3] B.H. Yilmaz, Sasakian manifolds satisfying certain conditions Q tensor, Journal of Geometry, vol.111, pp.1-10, (2020).
  • [4] M. Yıldırım, A new type characterizarion of Kenmotsu manifolds with respect to Q tensor, Journal of Geometry and Physics, vol.176, pp.104498, (2022).
  • [5] K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J., vol.24, pp.93-103, (1972).
  • [6] G.Pitis, Geometry of Kenmotsu Manifolds: Publishing House of Transilvania University of Bra¸sov, Bra¸sov, (2007).
  • [7] H. ¨ Ozturk, N. Aktan,C. Murathan, On α−Kenmotsu manifolds satisfying certain conditions, Applied sciences vol.12 , pp.115-126, (2010).
  • [8] N. Aktan, On non-existence of lightlike of indefinite Kenmotsu space form, Turkish journal of Math., vol.32 no.2, 127-139, (2008).
  • [9] N. Aktan, S. Balkan, M. Yıldırım, On weak symmetries of almost Kenmotsu (κ, μ, ν)-spaces, Hacettepe Journal of Mathematics and Statistics, vol.42 no.4, pp.447-453,(2013).
  • [10] G. Ayar, M. Yıldırım, η−Ricci Solitons on nearly Kenmotsu manifolds, Asian-Eur. J. Math., vol.12 no.6,pp. 2040002,(2019).
  • [11] M. Yıldırım, On Non-Existence of Weakly Symmetric Nearly Kenmotsu Manifold with Semisymmetric Metric Connection, Konuralp Journal of Mathematics, vol.9 no.2, pp. 332-336, (2021).
  • [12] N. Tanaka, On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections, Japan. J. Math. New series, 2 (1976), 131–190.
  • [13] S. M. Webster, Pseudo-Hermitian structures on a real hypersurface, J. Differ. Geom. 13 (1978), 25–41.
  • [14] S. Tanno, Variational problems on contact Riemannian manifolds, Trans. Amer. Math. Soc. 314 n. 1 (1989), 349–379.
  • [15] Blair, D.E.: Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics , Springer-Verlag, Berlin,(1976)
  • [16] Kıran Kumar, D. L., Nagaraja, H. G. ve Kumari, D., 2019. Concircular curvature tensor of Kenmotsu Manifolds admitting generalized Tanaka-Webster connection, J. Math. Comput. Sci., 9, 4, 447-462.
  • [17] Tanno, S.: The automorphism groups of almost contact Riemannian manifolds. Tohoku Math, J., 21,21-38, (1969)
  • [18] G. Ghosh and U. C. De, Kenmotsu manifolds with generalized Tanaka-Webster connection, Publications de l’Institut Mathematique-Beograd, 102 (2017), 221–230.
Year 2022, , 122 - 128, 31.07.2022
https://doi.org/10.33773/jum.1134765

Abstract

References

  • [1] C.A. Mantica, Y.J. Suh, Pseudo Q−symmetric Riemannian manifolds. Int. J. Geom. Methods Mod. Phys. vol.10, pp.1-25, (2013).
  • [2] C.A. Mantica, L.G. Molinari, Riemann compatible tensors. Colloq. Math.vol.128 No.2, pp.197-200, (2012).
  • [3] B.H. Yilmaz, Sasakian manifolds satisfying certain conditions Q tensor, Journal of Geometry, vol.111, pp.1-10, (2020).
  • [4] M. Yıldırım, A new type characterizarion of Kenmotsu manifolds with respect to Q tensor, Journal of Geometry and Physics, vol.176, pp.104498, (2022).
  • [5] K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J., vol.24, pp.93-103, (1972).
  • [6] G.Pitis, Geometry of Kenmotsu Manifolds: Publishing House of Transilvania University of Bra¸sov, Bra¸sov, (2007).
  • [7] H. ¨ Ozturk, N. Aktan,C. Murathan, On α−Kenmotsu manifolds satisfying certain conditions, Applied sciences vol.12 , pp.115-126, (2010).
  • [8] N. Aktan, On non-existence of lightlike of indefinite Kenmotsu space form, Turkish journal of Math., vol.32 no.2, 127-139, (2008).
  • [9] N. Aktan, S. Balkan, M. Yıldırım, On weak symmetries of almost Kenmotsu (κ, μ, ν)-spaces, Hacettepe Journal of Mathematics and Statistics, vol.42 no.4, pp.447-453,(2013).
  • [10] G. Ayar, M. Yıldırım, η−Ricci Solitons on nearly Kenmotsu manifolds, Asian-Eur. J. Math., vol.12 no.6,pp. 2040002,(2019).
  • [11] M. Yıldırım, On Non-Existence of Weakly Symmetric Nearly Kenmotsu Manifold with Semisymmetric Metric Connection, Konuralp Journal of Mathematics, vol.9 no.2, pp. 332-336, (2021).
  • [12] N. Tanaka, On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections, Japan. J. Math. New series, 2 (1976), 131–190.
  • [13] S. M. Webster, Pseudo-Hermitian structures on a real hypersurface, J. Differ. Geom. 13 (1978), 25–41.
  • [14] S. Tanno, Variational problems on contact Riemannian manifolds, Trans. Amer. Math. Soc. 314 n. 1 (1989), 349–379.
  • [15] Blair, D.E.: Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics , Springer-Verlag, Berlin,(1976)
  • [16] Kıran Kumar, D. L., Nagaraja, H. G. ve Kumari, D., 2019. Concircular curvature tensor of Kenmotsu Manifolds admitting generalized Tanaka-Webster connection, J. Math. Comput. Sci., 9, 4, 447-462.
  • [17] Tanno, S.: The automorphism groups of almost contact Riemannian manifolds. Tohoku Math, J., 21,21-38, (1969)
  • [18] G. Ghosh and U. C. De, Kenmotsu manifolds with generalized Tanaka-Webster connection, Publications de l’Institut Mathematique-Beograd, 102 (2017), 221–230.
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Mustafa Yıldırım 0000-0002-7885-1492

Ramazan Çınar Kaya 0000-0002-4517-9791

Publication Date July 31, 2022
Submission Date June 23, 2022
Acceptance Date July 29, 2022
Published in Issue Year 2022

Cite

APA Yıldırım, M., & Kaya, R. Ç. (2022). A NOTE ON KENMOTSU MANIFOLDS ADMITTING GENERALIZED TANAKA-WEBSTER CONNECTION. Journal of Universal Mathematics, 5(2), 122-128. https://doi.org/10.33773/jum.1134765
AMA Yıldırım M, Kaya RÇ. A NOTE ON KENMOTSU MANIFOLDS ADMITTING GENERALIZED TANAKA-WEBSTER CONNECTION. JUM. July 2022;5(2):122-128. doi:10.33773/jum.1134765
Chicago Yıldırım, Mustafa, and Ramazan Çınar Kaya. “A NOTE ON KENMOTSU MANIFOLDS ADMITTING GENERALIZED TANAKA-WEBSTER CONNECTION”. Journal of Universal Mathematics 5, no. 2 (July 2022): 122-28. https://doi.org/10.33773/jum.1134765.
EndNote Yıldırım M, Kaya RÇ (July 1, 2022) A NOTE ON KENMOTSU MANIFOLDS ADMITTING GENERALIZED TANAKA-WEBSTER CONNECTION. Journal of Universal Mathematics 5 2 122–128.
IEEE M. Yıldırım and R. Ç. Kaya, “A NOTE ON KENMOTSU MANIFOLDS ADMITTING GENERALIZED TANAKA-WEBSTER CONNECTION”, JUM, vol. 5, no. 2, pp. 122–128, 2022, doi: 10.33773/jum.1134765.
ISNAD Yıldırım, Mustafa - Kaya, Ramazan Çınar. “A NOTE ON KENMOTSU MANIFOLDS ADMITTING GENERALIZED TANAKA-WEBSTER CONNECTION”. Journal of Universal Mathematics 5/2 (July 2022), 122-128. https://doi.org/10.33773/jum.1134765.
JAMA Yıldırım M, Kaya RÇ. A NOTE ON KENMOTSU MANIFOLDS ADMITTING GENERALIZED TANAKA-WEBSTER CONNECTION. JUM. 2022;5:122–128.
MLA Yıldırım, Mustafa and Ramazan Çınar Kaya. “A NOTE ON KENMOTSU MANIFOLDS ADMITTING GENERALIZED TANAKA-WEBSTER CONNECTION”. Journal of Universal Mathematics, vol. 5, no. 2, 2022, pp. 122-8, doi:10.33773/jum.1134765.
Vancouver Yıldırım M, Kaya RÇ. A NOTE ON KENMOTSU MANIFOLDS ADMITTING GENERALIZED TANAKA-WEBSTER CONNECTION. JUM. 2022;5(2):122-8.