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Öğe A classification of a totally umbilical slant submanifold of cosymplectic manifolds(Hindawi Publishing Corporation, 2012) Uddin, Siraj; Özel, Cenap; Khan, Viqar AzamWe study slant submanifolds of a cosymplectic manifold. It is shown that a totally umbilical slant submanifold M of a cosymplectic manifold (M) over bar is either an anti-invariant submanifold or a 1-dimensional submanifold. We show that every totally umbilical proper slant submanifold of a cosymplectic manifold is totally geodesic.Öğe A Classification theorem on totally umbilical submanifolds in a cosymplectic manifold(2014) Uddin, Siraj; Özel, CenapIn the present paper, we study totally umbilical submanifolds of cosymplectic manifolds. We obtain a result on the classification of totallyumbilical contact CR-submanifolds of a cosymplectic manifold.Öğe A geometric inequality for warped product semi-slant submanifolds of nearly cosymplectic manifolds(Union Matematica Argentina, 2014) Uddin, Siraj; Mustafa, Abdulqader; Wong, Bernardine Renaldo; Özel, CenapRecently, we have shown that there do not exist warped product semislant submanifolds of cosymplectic manifolds [K.A. Khan, V.A. Khan and Siraj Uddin, Balkan J. Geom. Appl. 13 (2008), 55{65]. The nearly co- symplectic structure generalizes the cosymplectic one. Therefore the nearly Kaehler structure generalizes the Kaehler structure in almost Hermitian set- ting. It is interesting that the warped product semi-slant submanifolds exist in the nearly cosymplectic case while in the cosymplectic case they do not. In the beginning, we prove some preparatory results and finally we obtain an inequality such as {norm of matrix} h {norm of matrix} 2 ? 4q csc2 ?{1+ 1/9 cos2 ?}{norm of matrix} ?r ln f {norm of matrix} 2 in terms of intrinsic and extrinsic invariants. The equality case is also considered.Öğe Warped product submanifolds of LP-Sasakian manifolds(Hindawi Ltd, 2012) Hui, Shyamal Kumar; Uddin, Siraj; Özel, Cenap; Mustafa, A. A.We study of warped product submanifolds, especially warped product hemi-slant submanifolds of LP-Sasakian manifolds. We obtain the results on the nonexistance or existence of warped product hemi-slant submanifolds and give some examples of LP-Sasakian manifolds. The existence of warped product hemi-slant submanifolds of an LP-Sasakian manifold is also ensured by an interesting example.Öğe Warped product CR-submanifolds of Lorentzian ?-Kenmotsu manifolds(Publications L Institut Mathematique Matematicki, 2012) Uddin, Siraj; Özel, Cenap; Khan, Viqar AzamWe study the geometry of warped product submanifolds of Lorentzian-beta-Kenmotsu manifolds. We obtain a characterization result for CR-warped products.
