CHARACTERIZATIONS OF CONTACT PSEUDO-SLANT SUBMANIFOLDS OF A PARA-KENMOTSU MANIFOLD

Year 2022, Volume: 3 Issue: 1, 49 - 59, 30.06.2022

Süleyman Dirik , Ümit Yıldırım

https://doi.org/10.54559/jauist.1124012

Cited By: 2

Abstract

In this paper, the geometry of contact pseudo-slant submanifolds of a para Kenmotsu manifold
howe been studied. The necessary and sufficient conditions for a submanifolds to be a contact pseudoslant
submanifolds of a para Kenmotsu manifold are given.

Keywords

Para-Kenmotsu manifold, contact pseudo-slant submanifold, totally geodesic, totally umbilical

References

• [1] M. Atçeken and S.Dirik , On the geometry of pseudo-slant submanifold of a Kenmotsu manifold, Gulf Journal of Mathematics , 2(2)(2014),51-66.
• [2 D. E. Blair, Contact Manifolds in Riemannian Geometry: Lecture Notes in Mathematics, 509, Springer, Berlin (1976).
• [3] D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Birkhäuser, Boston (2002).
• [4] D. E. Blair, T. Koufogiorgos, B. J. Papantoniou, Contact metric manifolds satisfying a nullity condition, Israel Journal of Mathematics 91, (1995), 189-214.
• [5] J. L. Cabrerizo, A. Carriazo, L. M. Fernandez, M. Fernandez, Slant submanifolds in Sasakian manifolds, Glasgow Mathematical Journal, 42, (2000), 125-138.
• [6] A. Carriazo, New Devolopments in Slant Submanifolds Theory, Narosa publishing House, New Delhi, India, (2002).
• [7] A. Carriazo, V. Martin-Molina and M. M. Tripathi, Generalized (κ,μ)-space forms, Mediterranean Journal of Mathematics, 10, (2013), 475-496, doi: 10.1007/s00009-012-0196-2.
• [8] B. Y. Chen, Geometry of slant submanifolds, Katholieke Universiteit Leuven, Leuven, (1990).
• [9] B.Y. Chen, Slant immersions, Bulletin of the Australian Mathematical Society, 41, (1990), 135-147.
• [10] U.C. De and A. Sarkar, On Pseudo-slant submanifolds of trans-Sasakian manifolds, Proceedings of the Estonian Academy of Sciences, 60, 1(2011), 1-11, doi: 10.3176/proc.2011.1.01
• [11] S. Dirik, M. Atçeken, Pseudo-slant submanifolds in Cosymplectic space forms, Acta Universitatis Sapientiae: Mathematica, 8, 1(2016), 53-74, doi: 10.1515/ausm-2016-0004.
• [12] S. Dirik, M. Atçeken, ¨U . Yildirim, Pseudo-slant submanifold in Kenmotsu space forms, Journal of Advances in Mathematics, 11, 10(2016), 5680-5696.
• [13] V. A. Khan and M. A. Khan, Pseudo-slant submanifolds of a Sasakian manifold, Indian Journal of püre and applied Mathematics, 38, 1(2007), 31-42.
• [14] M. A. Khan, Totally umbilical Hemi-slant submanifolds of Cosymplectic manifolds, Mathematica Aeterna, 3, 8(2013), 645-653.
• [15] T. Koufogiorgos, Contact Riemannian manifolds with constant 𝜑-sectional curvature, Tokyo Journal of Mathematics, 20, 1(1997),13-22.
• [16] B. Laha and A. Bhattacharyya, Totally umbilical Hemislant submanifolds of LP-Sasakian Manifold, Lobachevskii Journal of Mathematics, 36, 2(2015), 127-131, doi: 10.1134/S1995080215020122.
• [17] A. Lotta, Slant submanifolds in contact geometry, Bulletin of Mathematical Society Romania, 39, (1996), 183-198.
• [18] S. Phan, On geometry of warped product pseudo-slant submanifolds on generelized Sasakian space forms , Gulf journal of Mathematics 9(1), (2020,)42-61.
• [19] M.S. Siddesha and C. S. Bagewadi, On Slant submanifolds of (κ,μ)−contact manifold, Differential Geometry-Dynamical Systems, 18, (2016), 123-131.
• [20] N. Venkatesha, Srikantha and M.S.Siddesha, On pseudo-slant submanifolds of (κ,μ)−contact space forms, Palestine Journal of Mathematics, 8(2)(2019) , 248-257.