WARPED PRODUCT SEMI-SLANT SUBMANIFOLD OF NEARLY QUASI SASAKIAN MANIFOLD
Keywords:
Warped product, slant submanifold, Semi-slant submanifold, Nearly quasi sasakian structure
Abstract
The main objective of this paper is to study some geometric properties of warped product semi-slant submanifold of a nearly quasi Sasakian manifold
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References
[1] Atceken M. (2011). Contact CR-warped product submanifolds in cosymplectic space forms, Collect. Math. 62, 17-26.
[2] Blair D.E. (1967). The theory of quasi-Sasakian structure, J. Differential Geo. 1, 331-345.
[3] Blair D.E. (1971). Almost contact manifolds with killing structure tensors I, Pac. J. Math. 39, 285-292.
[4] Blair D.E. and Yano K. (1971). Affine almost contact manifolds and f-manifolds with affine killing structure tensors, Kodai Math. Sem. Rep. 23, 473-479.
[5] Blair D.E. and Showers D.K. (1974). Almost contact manifolds with killing structures tensors II, J. Differ. Geom. 9, 577-582.
[6] Bishop R.L. and Neill B. O. (1969). Manifolds of negative curvature, Trans. Amer. Math. Soc. 145, 1-49.
[7] Cabrerizo J.L., Carriazo A., Fernandez L.M. and Fernandez M. (1999). Semi-slant submanifolds of a Sasakian manifold, Geom. Dedicata 78, 183-199.
[8] Cabrerizo J.L., Carriazo A., Fernandez L.M. and Fernandez M. (2000). Slant submanifolds in Sasakian manifolds, Glasgow Math. J. 42, 125-138.
[9] Chen B.Y.(2001). Geometry of warped product CR-submanifolds in Kaehler manifolds I, Monatsh. Math. 133, 177-195.
[10] Hasegawa I. and Mihai I. (2003). Contact CR-warped product submanifolds in Sasakian manifolds, Geom. Dedicata 102, 143-150.
[11] Kanemaki S. (1977). Quasi-Sasakian manifolds, Tohoku Math. J. 29, 227-233.
[12] Kanemaki S. (1984). On quasi-Sasakian manifolds, Differential Geometry Banach Center Publications 12, 95125.
[13] Khan K.A., Khan V.A. and Siraj Uddin (2008). Warped product submanifolds of cosymplectic manifolds, Balkan J. Geom. Appl. 13, 55-65.
[14] Kim B.H. (1990). Fibred Riemannian spaces with quasi-Sasakian structure, Hiroshima Math. J. 20, 477-513.
[15] Neill B. O. (1983). Semi-Riemannian geometry with application to Relativity, Academic Press, New York.
[16] Oubina J.A. (1985). New classes of almost contact metric structures, Publ. Math. Debrecen 32, 187-193.
[17] Papaghiuc N. (1994). Semi-slant submanifolds of Khaelerian manifolds, Ann. St. Univ. Iasi, 9, 55-61.
[18] Rahman S. and Shafiullah (2011). Geometry of Hypersurfaces of a Semi Symmetric Semi Metric Connection in a Quasi-Sasakian Manifold, Journal of Purvanchal Academy of Sciences, 17, 231-242.
[19] Rahman S. and Ahmad A. (2011). On The Geometry of Hypersurfaces of a Certain Connection in a Quasi-Sasakian Manifold, International Journal Mathematical Combinatorics 3, 23-33.
[20] Rahman S. (2011). Some Properties of Hyperbolic contact Manifold in a Quasi Sasakian Manifold, Turkic World Mathematical Society Journal of Applied and Engineering Mathematics 1(1), 41-48.
[21] Rahman S. (2014). Geometry of Hypersurfaces of a semi symmetric metric connection in a quasi-Sasakian manifold, Journal-Proceedings of the Institute of Applied Mathematics, 3 (2), 152-164.
[22] Rahman S. (2015), Geometry of hypersurfaces of a quarter semi symmetric non metric connection in a quasi-Sasakian manifold, Carpathian Mathematical Publications 7(2) 226-235 doi:10.15330/cmp.7.2.226-235.
[23] Rahman S. and Agrawal N.K. (2017). On the geometry of slant and pseudo-slant submanifolds in a quasi Sasakian manifolds, J. Modern Technology and Engineering 2(1), 82-89.
[24] Rahman S. (2017), Contact conformal connection on a geometry of hypersurfaces with certain connection in a quasi-Sasakian manifold, Bulletin of the Transilvania University of Brasov Series III: Mathematics, Informatics, Physics, 10 (59), 135-148.
[25] Siraj Uddin, Kon S. H., Khan M. A. and Singh Khushwant (2011). Warped product semi-invariant submanifolds of nearly cosymplectic manifolds, Math. Probl. Eng. 2011.
[26] Siraj Uddin and Khan K. A. (2012). An inequality for contact CR-warped product submanifolds of nearly cosympletic manifolds, J. Inequal. Appl. 304.
[27] Tanno S. (1971). Quasi-Sasakian structure of rank 2p + 1, J. Differential Geom. 5, 317-324.
[2] Blair D.E. (1967). The theory of quasi-Sasakian structure, J. Differential Geo. 1, 331-345.
[3] Blair D.E. (1971). Almost contact manifolds with killing structure tensors I, Pac. J. Math. 39, 285-292.
[4] Blair D.E. and Yano K. (1971). Affine almost contact manifolds and f-manifolds with affine killing structure tensors, Kodai Math. Sem. Rep. 23, 473-479.
[5] Blair D.E. and Showers D.K. (1974). Almost contact manifolds with killing structures tensors II, J. Differ. Geom. 9, 577-582.
[6] Bishop R.L. and Neill B. O. (1969). Manifolds of negative curvature, Trans. Amer. Math. Soc. 145, 1-49.
[7] Cabrerizo J.L., Carriazo A., Fernandez L.M. and Fernandez M. (1999). Semi-slant submanifolds of a Sasakian manifold, Geom. Dedicata 78, 183-199.
[8] Cabrerizo J.L., Carriazo A., Fernandez L.M. and Fernandez M. (2000). Slant submanifolds in Sasakian manifolds, Glasgow Math. J. 42, 125-138.
[9] Chen B.Y.(2001). Geometry of warped product CR-submanifolds in Kaehler manifolds I, Monatsh. Math. 133, 177-195.
[10] Hasegawa I. and Mihai I. (2003). Contact CR-warped product submanifolds in Sasakian manifolds, Geom. Dedicata 102, 143-150.
[11] Kanemaki S. (1977). Quasi-Sasakian manifolds, Tohoku Math. J. 29, 227-233.
[12] Kanemaki S. (1984). On quasi-Sasakian manifolds, Differential Geometry Banach Center Publications 12, 95125.
[13] Khan K.A., Khan V.A. and Siraj Uddin (2008). Warped product submanifolds of cosymplectic manifolds, Balkan J. Geom. Appl. 13, 55-65.
[14] Kim B.H. (1990). Fibred Riemannian spaces with quasi-Sasakian structure, Hiroshima Math. J. 20, 477-513.
[15] Neill B. O. (1983). Semi-Riemannian geometry with application to Relativity, Academic Press, New York.
[16] Oubina J.A. (1985). New classes of almost contact metric structures, Publ. Math. Debrecen 32, 187-193.
[17] Papaghiuc N. (1994). Semi-slant submanifolds of Khaelerian manifolds, Ann. St. Univ. Iasi, 9, 55-61.
[18] Rahman S. and Shafiullah (2011). Geometry of Hypersurfaces of a Semi Symmetric Semi Metric Connection in a Quasi-Sasakian Manifold, Journal of Purvanchal Academy of Sciences, 17, 231-242.
[19] Rahman S. and Ahmad A. (2011). On The Geometry of Hypersurfaces of a Certain Connection in a Quasi-Sasakian Manifold, International Journal Mathematical Combinatorics 3, 23-33.
[20] Rahman S. (2011). Some Properties of Hyperbolic contact Manifold in a Quasi Sasakian Manifold, Turkic World Mathematical Society Journal of Applied and Engineering Mathematics 1(1), 41-48.
[21] Rahman S. (2014). Geometry of Hypersurfaces of a semi symmetric metric connection in a quasi-Sasakian manifold, Journal-Proceedings of the Institute of Applied Mathematics, 3 (2), 152-164.
[22] Rahman S. (2015), Geometry of hypersurfaces of a quarter semi symmetric non metric connection in a quasi-Sasakian manifold, Carpathian Mathematical Publications 7(2) 226-235 doi:10.15330/cmp.7.2.226-235.
[23] Rahman S. and Agrawal N.K. (2017). On the geometry of slant and pseudo-slant submanifolds in a quasi Sasakian manifolds, J. Modern Technology and Engineering 2(1), 82-89.
[24] Rahman S. (2017), Contact conformal connection on a geometry of hypersurfaces with certain connection in a quasi-Sasakian manifold, Bulletin of the Transilvania University of Brasov Series III: Mathematics, Informatics, Physics, 10 (59), 135-148.
[25] Siraj Uddin, Kon S. H., Khan M. A. and Singh Khushwant (2011). Warped product semi-invariant submanifolds of nearly cosymplectic manifolds, Math. Probl. Eng. 2011.
[26] Siraj Uddin and Khan K. A. (2012). An inequality for contact CR-warped product submanifolds of nearly cosympletic manifolds, J. Inequal. Appl. 304.
[27] Tanno S. (1971). Quasi-Sasakian structure of rank 2p + 1, J. Differential Geom. 5, 317-324.
Published
2019-01-02
How to Cite
Rahman, S., Khan, M., & Horaira, A. (2019). WARPED PRODUCT SEMI-SLANT SUBMANIFOLD OF NEARLY QUASI SASAKIAN MANIFOLD. Boson Journal of Modern Physics, 5(1), 443-453. Retrieved from https://scitecresearch.com/journals/index.php/bjmp/article/view/1667
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