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On almost α-para-Kenmotsu manifolds satisfyıng certain conditions

Year 2019, Volume: 68 Issue: 1, 559 - 571, 01.02.2019
https://doi.org/10.31801/cfsuasmas.438369

Abstract

In this paper, we study some remarkable properties of almost α-para-Kenmotsu manifolds. We consider projectively flat, conformally flat and concircularly flat almost α-para-Kenmotsu manifolds (with the η-parallel tensor field φh). Finally, we present an example to verify our results.

References

  • Bejan, C.L., Almost parahermitian structures on the tangent bundle of an almost para-coHermitian manifold, In: The Proceedings of the Fifth National Seminar of Finsler and Lagrange Spaces (Bra sov, 1988), 105--109, Soc. Stiinte Mat. R. S. Romania, Bucharest, 1989.
  • Boeckx, E. and Cho, J. T., η-parallel contact metric spaces, Differ. Geom. Appl. 22, (2005), 275-285. BuchRosc : Buchner, K. and Rosca, R., Variétes para-coKählerian á champ concirculaire horizontale, C. R. Acad. Sci. Paris 285 (1977), Ser. A, 723-726.
  • Buchner, K. and Rosca, R., Co-isotropic submanifolds of a para-coKählerian manifold with concicular vector field, J. Geometry, 25 (1985), 164-177.
  • Cappelletti-Montano, B., Küpeli Erken, I. and Murathan, C., Nullity conditions in paracontact geometry, Diff. Geom. Appl. 30 (2012), 665-693.
  • Dacko, P., On almost para-cosymplectic manifolds, Tsukuba J. Math. 28 (2004), 193-213. kaneyuki1 : Kaneyuki, S. and Williams, F. L., Almost paracontact and parahodge structures on manifolds, Nagoya Math. J 1985; 99: 173-187.
  • Küpeli Erken, I., Dacko, P. and Murathan, C., Almost α-paracosymplectic manifolds, J. Geom. Phys., 88 (2015) 30-51. HAKAN : Öztürk, H., Aktan, N. and Murathan, C., Almost α-cosymplectic (κ,μ,ν)-spaces, Submitted. Available in Arxiv:1007.0527 [math. DG].
  • Öztürk, H., Murathan, C., Aktan, N. and Turgut Vanlı, A., Almost α-cosymplectic f-manifolds, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 60 no. 1, (2014), 211-226.
  • Rossca, R. and Vanhecke, L., Súr une variété presque paracokählérienne munie d'une connexion self-orthogonale involutive, Ann. Sti. Univ. "Al. I. Cuza" Ia si 22 (1976), 49-58.
  • Soos, G., Über die geodätischen Abbildungen von Riemannaschen Räumen auf projektiv symmetrische Riemannsche Räume, Acta. Math. Acad. Sci. Hungar. Tom 9 (1958), 359-361.
  • Wełyczko, J., On basic curvature identities for almost (para)contact metric manifolds. Available in Arxiv: 1209.4731 [math. DG].
  • Yano, K., Concircular geometry I, Concircular transformations, Proc. Imp. Acad. Tokyo, 16 (1940), 195-200.
  • Yano, K. and Kon, M., Structures on manifolds, Series in Pure Mathematics, 3. World Scientific Publishing Co., Singapore, (1984).
  • Yano, K. and Bochner, S., Curvature and Betti numbers, Annals of mathematics studies, 32, Princeton University Press,1953.
  • Zamkovoy, S., Canonical connections on paracontact manifolds, Ann. Glob. Anal. Geom. 36 (2009), 37-60.
Year 2019, Volume: 68 Issue: 1, 559 - 571, 01.02.2019
https://doi.org/10.31801/cfsuasmas.438369

Abstract

References

  • Bejan, C.L., Almost parahermitian structures on the tangent bundle of an almost para-coHermitian manifold, In: The Proceedings of the Fifth National Seminar of Finsler and Lagrange Spaces (Bra sov, 1988), 105--109, Soc. Stiinte Mat. R. S. Romania, Bucharest, 1989.
  • Boeckx, E. and Cho, J. T., η-parallel contact metric spaces, Differ. Geom. Appl. 22, (2005), 275-285. BuchRosc : Buchner, K. and Rosca, R., Variétes para-coKählerian á champ concirculaire horizontale, C. R. Acad. Sci. Paris 285 (1977), Ser. A, 723-726.
  • Buchner, K. and Rosca, R., Co-isotropic submanifolds of a para-coKählerian manifold with concicular vector field, J. Geometry, 25 (1985), 164-177.
  • Cappelletti-Montano, B., Küpeli Erken, I. and Murathan, C., Nullity conditions in paracontact geometry, Diff. Geom. Appl. 30 (2012), 665-693.
  • Dacko, P., On almost para-cosymplectic manifolds, Tsukuba J. Math. 28 (2004), 193-213. kaneyuki1 : Kaneyuki, S. and Williams, F. L., Almost paracontact and parahodge structures on manifolds, Nagoya Math. J 1985; 99: 173-187.
  • Küpeli Erken, I., Dacko, P. and Murathan, C., Almost α-paracosymplectic manifolds, J. Geom. Phys., 88 (2015) 30-51. HAKAN : Öztürk, H., Aktan, N. and Murathan, C., Almost α-cosymplectic (κ,μ,ν)-spaces, Submitted. Available in Arxiv:1007.0527 [math. DG].
  • Öztürk, H., Murathan, C., Aktan, N. and Turgut Vanlı, A., Almost α-cosymplectic f-manifolds, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 60 no. 1, (2014), 211-226.
  • Rossca, R. and Vanhecke, L., Súr une variété presque paracokählérienne munie d'une connexion self-orthogonale involutive, Ann. Sti. Univ. "Al. I. Cuza" Ia si 22 (1976), 49-58.
  • Soos, G., Über die geodätischen Abbildungen von Riemannaschen Räumen auf projektiv symmetrische Riemannsche Räume, Acta. Math. Acad. Sci. Hungar. Tom 9 (1958), 359-361.
  • Wełyczko, J., On basic curvature identities for almost (para)contact metric manifolds. Available in Arxiv: 1209.4731 [math. DG].
  • Yano, K., Concircular geometry I, Concircular transformations, Proc. Imp. Acad. Tokyo, 16 (1940), 195-200.
  • Yano, K. and Kon, M., Structures on manifolds, Series in Pure Mathematics, 3. World Scientific Publishing Co., Singapore, (1984).
  • Yano, K. and Bochner, S., Curvature and Betti numbers, Annals of mathematics studies, 32, Princeton University Press,1953.
  • Zamkovoy, S., Canonical connections on paracontact manifolds, Ann. Glob. Anal. Geom. 36 (2009), 37-60.
There are 14 citations in total.

Details

Primary Language English
Journal Section Review Articles
Authors

İrem Küpeli Erken 0000-0003-4471-3291

Publication Date February 1, 2019
Submission Date December 20, 2017
Acceptance Date June 28, 2018
Published in Issue Year 2019 Volume: 68 Issue: 1

Cite

APA Küpeli Erken, İ. (2019). On almost α-para-Kenmotsu manifolds satisfyıng certain conditions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 559-571. https://doi.org/10.31801/cfsuasmas.438369
AMA Küpeli Erken İ. On almost α-para-Kenmotsu manifolds satisfyıng certain conditions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2019;68(1):559-571. doi:10.31801/cfsuasmas.438369
Chicago Küpeli Erken, İrem. “On Almost α-Para-Kenmotsu Manifolds satisfyıng Certain Conditions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 1 (February 2019): 559-71. https://doi.org/10.31801/cfsuasmas.438369.
EndNote Küpeli Erken İ (February 1, 2019) On almost α-para-Kenmotsu manifolds satisfyıng certain conditions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 559–571.
IEEE İ. Küpeli Erken, “On almost α-para-Kenmotsu manifolds satisfyıng certain conditions”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 559–571, 2019, doi: 10.31801/cfsuasmas.438369.
ISNAD Küpeli Erken, İrem. “On Almost α-Para-Kenmotsu Manifolds satisfyıng Certain Conditions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 2019), 559-571. https://doi.org/10.31801/cfsuasmas.438369.
JAMA Küpeli Erken İ. On almost α-para-Kenmotsu manifolds satisfyıng certain conditions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:559–571.
MLA Küpeli Erken, İrem. “On Almost α-Para-Kenmotsu Manifolds satisfyıng Certain Conditions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, 2019, pp. 559-71, doi:10.31801/cfsuasmas.438369.
Vancouver Küpeli Erken İ. On almost α-para-Kenmotsu manifolds satisfyıng certain conditions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):559-71.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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