Totally umbilical proper slant submanifolds of para-Kenmotsu manifold
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M.S. Siddesha
mssiddesha@gmail.com
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C.S. Bagewadi
prof_bagewadi@yahoo.co.in
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D. Nirmala
nirmaladraj14@gmail.com
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DOI:
https://doi.org/10.4067/S0719-06462019000200041Abstract
In this paper, we study slant submanifolds of a para-Kenmotsu manifold. We prove that totally umbilical slant submanifold of a para-Kenmotsu manifold is either invariant or anti-invariant or dimension of submanifold is 1 or the mean curvature vector H of the submanifold lies in the invariant normal subbundle.
Keywords
[1] A.M. Blaga, Invariant, anti-invariant and slant submanifolds of a para-Kenmotsu manifold, BSG Proceedings, 24 (2017), 19-28.
[2] A.M. Blaga, Eta-Ricci solitons on para-Kenmotsu manifolds, Balkan Journal of Geometry and Its Applications, 20(1) (2015), 1-13.
[3] J.L. Cabrerizo, A. Carriazo and L.M. Fernandez, Slant submanifolds in Sasakian manifolds, Glasgow Math. J., 42 (2000), 125-138.
[4] B.Y. Chen, Slant immersions, Bull. Aust. Math. Soc., 41 (1990), 135-147.
[5] B.Y. Chen, Geometry of slant submanifolds, Katholieke Universiteit Leuven, (1990).
[6] P. Dacko and Z. Olszak, On weakly para-cosymplectic manifolds of dimension 3, J. Geom. Phys., 57 (2007), 561-570.
[7] R.S. Gupta, S.M. Khursheed Haider and M.H. Shahid, Slant submanifolds of a Kenmotsu manifold, Radovi Matematicki, Vol. 12 (2004), 205-214.
[8] R.S. Gupta and P.K. Pandey, Structure on a slant submanifold of a Kenmotsu manifold, Differential Geometry - Dynamical Systems, 10 (2008), 139-147.
[9] S. Ivanov, D. Vassilev and S. Zamkovoy, Conformal paracontact curvature and the local flatness theorem, Geom. Dedicata, 144 (2010), 79-100.
[10] K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J., 24 (1972), 93-103.
[11] M.A. Khan, S. Uddin and K. Singh, A classification on totally umbilical proper slant and hemi- slant submanifolds of a nearly trans-Sasakian manifold, Differential Geometry Dynamical Systems, 13 (2011), 117-127.
[12] A. Lotta, Slant submanifolds in contact geometry, Bull. Math. Soc. Roum., 39 (1996), 183-198.
[13] A. Lotta, Three dimensional slant submanifolds of K-contact manifolds, Balkan J. Geom. Appl., 3(1) (1998), 37-51.
[14] M.S. Siddesha and C.S. Bagewadi, On slant submanifolds of (k, μ)-contact manifold, Differ- ential Geometry-Dynamical Systems, 18 (2016), 123-131.
[15] M.S. Siddesha and C.S. Bagewadi, Semi-slant submanifolds of (k, μ)-contact manifold, Com- mun. Fac. Sci. Univ. Ser. A1 Math. Stat., 67(2) (2017), 116-125.
[2] A.M. Blaga, Eta-Ricci solitons on para-Kenmotsu manifolds, Balkan Journal of Geometry and Its Applications, 20(1) (2015), 1-13.
[3] J.L. Cabrerizo, A. Carriazo and L.M. Fernandez, Slant submanifolds in Sasakian manifolds, Glasgow Math. J., 42 (2000), 125-138.
[4] B.Y. Chen, Slant immersions, Bull. Aust. Math. Soc., 41 (1990), 135-147.
[5] B.Y. Chen, Geometry of slant submanifolds, Katholieke Universiteit Leuven, (1990).
[6] P. Dacko and Z. Olszak, On weakly para-cosymplectic manifolds of dimension 3, J. Geom. Phys., 57 (2007), 561-570.
[7] R.S. Gupta, S.M. Khursheed Haider and M.H. Shahid, Slant submanifolds of a Kenmotsu manifold, Radovi Matematicki, Vol. 12 (2004), 205-214.
[8] R.S. Gupta and P.K. Pandey, Structure on a slant submanifold of a Kenmotsu manifold, Differential Geometry - Dynamical Systems, 10 (2008), 139-147.
[9] S. Ivanov, D. Vassilev and S. Zamkovoy, Conformal paracontact curvature and the local flatness theorem, Geom. Dedicata, 144 (2010), 79-100.
[10] K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J., 24 (1972), 93-103.
[11] M.A. Khan, S. Uddin and K. Singh, A classification on totally umbilical proper slant and hemi- slant submanifolds of a nearly trans-Sasakian manifold, Differential Geometry Dynamical Systems, 13 (2011), 117-127.
[12] A. Lotta, Slant submanifolds in contact geometry, Bull. Math. Soc. Roum., 39 (1996), 183-198.
[13] A. Lotta, Three dimensional slant submanifolds of K-contact manifolds, Balkan J. Geom. Appl., 3(1) (1998), 37-51.
[14] M.S. Siddesha and C.S. Bagewadi, On slant submanifolds of (k, μ)-contact manifold, Differ- ential Geometry-Dynamical Systems, 18 (2016), 123-131.
[15] M.S. Siddesha and C.S. Bagewadi, Semi-slant submanifolds of (k, μ)-contact manifold, Com- mun. Fac. Sci. Univ. Ser. A1 Math. Stat., 67(2) (2017), 116-125.
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Published
2019-08-10
How to Cite
[1]
M. . Siddesha, C. . Bagewadi, and D. . Nirmala, “Totally umbilical proper slant submanifolds of para-Kenmotsu manifold”, CUBO, vol. 21, no. 2, pp. 41–49, Aug. 2019.
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