×

Quasi hemi-slant submanifolds of cosymplectic manifolds. (English) Zbl 1447.53052

Summary: We introduce and study quasi hemi-slant submanifolds of almost contact metric manifolds (especially, cosymplectic manifolds) and validate their existence by providing some non-trivial examples. Necessary and sufficient conditions for integrability of distributions, which are involved in the definition of quasi hemi-slant submanifolds of cosymplectic manifolds, are obtained. Also, we investigate necessary and sufficient conditions for quasi hemi-slant submanifolds of cosymplectic manifolds to be totally geodesic and study the geometry of foliations determined by the distributions.

MSC:

53C40 Global submanifolds
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53D15 Almost contact and almost symplectic manifolds
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] A. Ali, and C. Ozel, Geometry of warped product pointwise semi-slant submanifolds of cosymplectic manifolds and its applications, Int. J. Geom. Meth. Mod. Phy. 14 (2017), 1750042. · Zbl 1362.53062
[2] A. Ali, S. Uddin and W. A. O. Othmam, Geometry of warped product pointwise semi-slant submanifold in Kaehler manifolds, Filomat 31 (2017), 3771-3788. · Zbl 1488.53176
[3] G. Ayar and S. K. Chaubey, M-projective curvature tensor over cosymplectic manifolds, Differential Geometry - Dynamical Systems. 21 (2019), 23-33. · Zbl 1423.53097
[4] M. Barbero-Linan, et al.: Unified formalison for nonautonomous mechanical systems. J. Math. Phys. 49 ()2008, 062902-062914. · Zbl 1152.81326
[5] 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. · Zbl 0463.53030
[6] A. M. Blaga, Invariant, anti-invariant and slant submanifolds of para-Kenmotsu manifold, BSG Publ. 24 (2017), 125-138. · Zbl 1390.53019
[7] D. E. Blair, Contact manifold in Riemannian geometry, Lecture notes in Math. 509 Springer-Verlag, New-York, (1976). · Zbl 0319.53026
[8] D. E. Blair and S. I. Goldberg, Topology of almost contact manifolds, J. Differential Geometry 1 (1967), 347-354. · Zbl 0163.43902
[9] J. L. Cabrerizo, A. Carriazo and L. M. Fernandez, Slant submanifolds in Sasakian manifolds, Glasg. Math. J. 42 (2000), 125-138. · Zbl 0957.53022
[10] B. Y. Chen, Geometry of slant submanifolds, Katholieke Universiteit, Leuven, (1990). · Zbl 0716.53006
[11] D. Chinea, M. De-Leon, and J. C. Marrero, Topology of cosymplectic manifolds, J. Math. Pures Appl. (9) 72 (1993), 567-591. · Zbl 0845.53025
[12] M. De-Leon, E. Merino, J. A. Oubina, P. R. Rodrigues and M. Salgado, Hamiltonian system on K−cosymplectic manifolds, J. Math. Phys. 39(1998), 876-893. · Zbl 0910.53022
[13] U. C. De and A. Sarkar, On pseudo-slant submanifolds of trans-Sasakian manifolds, Proc. Esto. Acad. sci. 60 (2011), 1-11. · Zbl 1230.53021
[14] U. C. De and A. A. Shaikh, Complex manifolds and Contact manifolds, Narosa Publ. House, (2009). · Zbl 1208.53001
[15] M. Kon, Remarks on anti-invariant submanifolds of a Sasakian manifold, Tensor (N.S.) 30 (1976), 239-245. · Zbl 0344.53016
[16] J. W. Lee and B. Sahin, Pointwise slant submersions, Bull Korean Math Soc. 51 (2014), 1115-1126. · Zbl 1296.53055
[17] A. Lotta, Slant submanifold in contact geometry, Bull. Math. Soc. Romanie 39 (1996), 183-198. · Zbl 0885.53058
[18] N. Papaghuic, Semi-slant submanifold of Kaehlerian manifold, An. St. Univ. AI. I. Cuza. Iasi. Math.(N.S.) 9 (1994), 55-61. · Zbl 0847.53012
[19] K. S. Park and R. Prasad, Semi-slant submersions, Bull. Korean Math. Soc. 50 (2013), 951-962. · Zbl 1273.53023
[20] B. Sahin, Warped product submanifolds of a Kaehler manifold with a slant factor, Ann. Pol. Math. 95 (2009), 107-126. · Zbl 1162.53040
[21] B. Sahin, Slant submersions from almost Hermitian manifolds, Bull. math. de la Soc. des Sciences Math. de Roumanie 54 (2011), 93-105. · Zbl 1224.53054
[22] F. Sahin, Cohomology of hemi-slant submanifolds of a Kaehler manifolds, J. Adv. Studies Topology 5 (2014), 27-31. · Zbl 1338.57021
[23] M. H. Shahid, et al., Slant submanifolds of cosymplectic manifold, Analele Stiintifice ale Universitatii Al I Cuza din Iasi - Matematica 50 (2004), 33-50. · Zbl 1074.53069
[24] S. S. Shukla and A. Yadav, Screen Pseudo-Slant Lightlike Submanifolds of Indefinite Sasakian Manifolds, Mediterranean Journal of Mathematics 13 (2016), 789-802. · Zbl 1338.53038
[25] S. Uddin, B. Y. Chen and F. R. Al-Solamy, Warped product bi-slant immersion in Kaehler manifolds, Mediterr. J. Math. 14 (2017), 14-95. · Zbl 1369.53039
[26] S. K. Yadav and S. K. Chaubey, Certain results on submanifolds of generalized Sasakian-space-forms, Honam Mathematical J. 42 (1) (2020), 123-137. · Zbl 1448.53021
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.