CR-submanifolds of SQ-Sasakian manifold

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Published: May 1, 2023
DOI: https://doi.org/10.5556/j.tkjm.54.2023.4656
Keywords:
Pseudo parallel Ricci soliton Yamabe soliton

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Sarvesh Kumar Yadav
Shyamal Kumar Hui
The University of Burdwan
Mohd. Iqbal
Pradip Mandal
Mohd. Aslam

Abstract

In this paper we discussed CR-submanifold of SQ-Sasakian manifold. Next, we considered Chaki pseudo parallel as well as Deszcz pseudo parallel CR-submanifold of SQ-Sasakian manifold. Further we studied almost Ricci soliton and almost Yamabe soliton with torse forming vector field on CR-subamnifold of SQ-Sasakian manifold using semi-symmetric metric connection.

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How to Cite
Yadav, S. K. ., Hui, S. K., Iqbal, M., Mandal, P., & Aslam, M. . (2023). CR-submanifolds of SQ-Sasakian manifold. Tamkang Journal of Mathematics, 54(2), 121–138. https://doi.org/10.5556/j.tkjm.54.2023.4656
Issue
Vol. 54 No. 2 (2023)
Section
Papers
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This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Author Biography

Shyamal Kumar Hui, The University of Burdwan

Associate Professor, Mathematics Department

References

M. A. Akyol, L. M. Fernandez, A. P. Martin, The L-sectional curvature of S-manifolds, Konuralp Journal of Mathematics, 4 (1) (2016), 246-253.

M. A. Akyol, R. Sar, On CR-submanifolds of S-manifolds endowed with a semi-symmetric non-metric connection, Commun. Fak. Sci. Univ. Ser. A1. Math. Stat., 65 (1) (2016), 171-185.

M. A. Akyol, A. T. Vanl and L. M. Fernandez, Semi-symmetric properties of S-manifolds endowed with a semi-symmetric non-metric connection, Annals of the Alexandru Ioan Cuza University-Mathematics, LX1 (2), (2015), 445-464.

A. C. Asperti, G. A. Lobos and F. Mercuri, Pseudo-parallel immersions in space forms, Mat. Contemp., 17 (1999), 59-70.

A. C. Asperti, G. A. Lobos and F. Mercuri, Pseudo-parallel submanifolds of a space forms, Adv. Geom., 2 (2002), 57-71.

M. Atceken, Contact CR-submanifolds of Kenmotsu manifolds, Serdica Math. J., 37 (2011), 67-78.

E. Barbosa, E. Riberio, On conformal solution of the Yamabe flow, Arch. Math., 101 (2013), 79-89.

A. Bejancu, CR-submanifolds of Kahler manifold I, Proc. Amer. Math. Soc., 69 (1978), 135-142.

A. Bejancu, CR-submanifolds of Kahler manifold II, Trans. Amer.Math.Soc., 250 (1979), 333-345.

D. E. Blair, The theory of quasi-Sasakian structure, J. Di er. Geom., 1 (1967), 331-345.

R. Deszcz, L. Verstraelen and S. Yaprak, Pseudosymmetric hypersurfaces in 4-dimensional Space of Constant Curvature, Bull. Ins. Math. Acad. Sinica, 22 (1994), 167-179.

L. M. Fernandez, CR-products of S-manifolds, Portugaliae Mathematica, 47 Fasc. 2- (1990).

A. Friedmann and J. A. Schouten, Über die Geometric der halbsymmetricschen Ubertragung, Math. Z., 21 (1924), 211-223.

S. K. Hui and P. Mandal, Pseudo parallel contact CR-submanifolds of Kenmotsu manifolds, Indian J. of Math., 59 (3) (2017), 385-402.

S. K. Hui and J. Roy, Invariant and anti-invariant submanifold of special quasi-Sasakian manifolds, J. Geom., 109 (2018), 37-53.

M. Kobayashi, Submanifolds of Sasakian manifold, Tensor, N. S., 35 (1981), 297-307.

J. H. Kwon, B. H. Kim A new class of almost contact Riemannian manifolds, Commun. Korean Math. Soc., 8 (1993), 455-465.

I. Mihai, CR-subvarietati ale unei f-varitati cu reperr complementare, Stud. Cerc. Math., 5 (1984), 435-443.

Z. Olszak, On three dimensional conformally flat quasi-Sasakian manifolds, Periodica Math. Hung., 59 (2009), 119-146.

L. Ornea, Subvarietati Cauchy-Riemann generice in S-varietati, Stud. Cerc. Mat 36 (1984), 435-443.

S. Pigola, M. Rigoli, M. Rimoldi and A. G. Setti, Ricci almost solitons, Ann. Sc. Norm. Super Pisa. Cl. Sci, 10 (2011), 757-799.

R. Sar, M. A. Akyol, E. Aksoy, Some curvature properties of CR-submanifolds of an S-manifold with a Quarter-symmetric non-metric connection, International Journal of Applied Mathematics and Statistics, 56 (3) (2017), 93-102.

R. Sar, M. A. Akyol, E. Aksoy, Some properties of CR-submanifolds of an S-manifold with a semi-symmetric metric connection, Celal Bayar University Journal of Science, 13 (3) (2017), 729-736.

M. H. Shahid, CR-submanifolds of Sasakian manifold, Review research Fac. Sc. Yugoslavia, 15 (1985), 203-178.

M. H. Shahid, CR-submanifolds of trans-Sasakian manifold I, Ind. J. Pure and Appl. Math, 22 (1991), 1007-1012.

M. H. Shahid, CR-submanifolds of trans-Sasakian manifold II, Ind. J. Pure and Appl. Math, 25 (1994), 299-307.

M. H. Shahid, CR-submanifolds of a Sasakian manifold with vanishing contact Bochner curvature tensor, Ind. J. Pure and Appl. Math., 21 (1990), 21-26.

A. A. Shaikh, On pseudo quasi-Einstein manifolds, Periodica Math. Hungarica, 59 (2009), 119-146.

A. A. Shaikh and H. Ahmad, On special quasi-Sasakian manifolds, Tensor N. S., 74 (2013), 13-33.

M. Shoeb, M. H. Shahid and A. Sharfuddin, On Submanifolds of a cosymplectic Manifold, Soochow Journal of Math., 27 (2) (2001), 161-174.

S. K. Yadav, O. Bahadir and S. K. Chaubey, Almost Yamabe solitons on LP-Sasakian manifolds with generalized symmetric metric connection of type (α, β), Balkan J. of Geom. and App., 25 (2) (2020), 124-139.

K. Yano, On a structure f satisfying $f^3 + f = 0$, Technical Report No. 12, University of Washington, Washington-USA, (1961).

K. Yano, M. Kon, Di erential geometry of CR-submanifolds, Geometrica Dedicata, 10 (1981), 369-391.

K. Yano, On torse forming direction in a Riemannian space, Proc. Imp. Acad. Tokoyo, 20 (1944), 340-345.

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