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http://dx.doi.org/10.5831/HMJ.2020.42.4.795

QUASI HEMI-SLANT SUBMANIFOLDS OF KAEHLER MANIFOLDS  

Prasad, Rajendra (Department of Mathematics and Astronomy University of Lucknow)
Shukla, S.S. (Department of Mathematics University of Allahabad)
Haseeb, Abdul (Department of Mathematics, Faculty of Science Jazan University)
Kumar, Sumeet (Department of Mathematics and Astronomy University of Lucknow)
Publication Information
Honam Mathematical Journal / v.42, no.4, 2020 , pp. 795-809 More about this Journal
Abstract
In the present paper, we introduce the notion of quasi hemi-slant submanifolds of almost Hermitian manifolds and give some of its examples. We obtain the necessary and sufficient conditions for the distributions to be integrable. We also investigate the necessary and sufficient conditions for these submanifolds to be totally geodesic and study the geometry of foliations determined by the distributions. Finally, we obtain the necessary and sufficient condition for a quasi hemi-slant submanifold to be local product of Riemannian manifold.
Keywords
Kaehler manifolds; Quasi hemi-slant submanifolds; totally geodesic;
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1 L. S. Das, M. Ahmad and A. Haseeb, On semi-invariant submanifolds of a nearly Sasakian manifold admitting a semi-symmetric non-metric connection, Journal of Applied Analysis, 17(2011), 119-130.   DOI
2 D. E. Blair, Contact manifold in Riemannian geometry, Lecture notes in Math. 509, Springer-Verlag, New-York, 1976.
3 J. L. Cabrerizo, A. Carriazo and L.M. Fernandez, Slant submanifolds in Sasakian manifolds, Glasg. Math. J., 42(2000), 125-138.   DOI
4 B. Y. Chen, Geometry of slant submanifolds, Katholieke Universiteit, Leuven, 1990.
5 U. C. De and P. Majhi, On invariant submanifolds of Kenmotsu manifolds, Journal of Geometry, 106 (2015), 109-122.   DOI
6 U. C. De, Y. Matsuyama and A. K. Sengupta, Generalized CR-submanifolds of a T-manifold, J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math., 11 (2004), 175-187.
7 U. C. De and A.A. Shaikh, Complex manifolds and Contact manifolds, Narosa Publ. House, New Delhi, 2009.
8 M. Kon, Remarks on anti-invariant submanifolds of a Sasakian manifold, Tensor (N.S.), 30 (1976), 239-245.
9 A. Lotta, Slant submanifold in contact geometry, Bull. Math. Soc. Romanie, 39(1996), 183-198.
10 N. Papaghuic, Semi-slant submanifold of Kaehlerian manifold, An. St. Univ. AI. I. Cuza. Iasi. Math.(N.S.), 9(1994) 55-61.
11 A. Benjancu and N. Papaghuic, Semi-invariant Submanifolds of a Sasakian manifold, An. St. Univ. AI. I. Cuza. Iasi. Math.(N.S.), 27(1981), 163-170.
12 K. S. Park and R. Prasad, Semi-slant submersions, Bull. Korean Math. Soc., 50 (2013), 951-962.   DOI
13 M. H. Shahid, On semi-invariant submanifolds of a nearly Sasakian manifold, Indian J. Pure and Appl. Math., 94 (10) (1993), 571-580.
14 H. M. Tastan, B. Sahin and S. Yanan, Hemi-slant submanifolds, Mediterr. J. Math., 13 (2016), 2171-2184.   DOI
15 Y. Tashiro, On contact structures of Hypersurfaces in Almost complex manifolds I, Tohoku Math. J., 15 (1963), 62-78.   DOI
16 M. H. Shahid, Some results on anti-invariant submanifolds of a trans-Sasakian manifold, Bull. Malays. Math. Sci. Soc., 27 (2004), 117-127.