On almost α-para-Kenmotsu manifolds satisfyıng certain conditions

İrem Küpeli Erken

doi:10.31801/cfsuasmas.438369

Research Article

On almost α-para-Kenmotsu manifolds satisfyıng certain conditions

Year 2019, Volume: 68 Issue: 1, 559 - 571, 01.02.2019

İrem Küpeli Erken

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.

Keywords

Almost α-para-Kenmotsu manifold, projectively flat, conformally flat, concircularly flat

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

İrem Küpeli Erken

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.