%0 Journal Article %T Contact CR-warped product submanifolds of a generalized Sasakian space form admitting a nearly Sasakian structure %A Ishan, Amira A. %A Khan, Meraj Ali %J Journal of Nonlinear Sciences and Applications %D 2019 %V 12 %N 7 %@ ISSN 2008-1901 %F Ishan2019 %X This paper studies the contact CR-warped product submanifolds of a generalized Sasakian space form admitting a nearly Sasakian structure. Some Characterization of the existence of these warped product submanifolds are also obtained. We illustrate that the warping function is a harmonic function under certain conditions. Moreover, a sharp estimate for the squared norm of the second fundamental form is investigated, and the equality case is also discussed. The results obtained in this paper generalize the results that have appeared in [I. Hasegawa, I. Mihai, Geom. Dedicata, \({\bf 102}\) (2003), 143--150], [I. Mihai, Geom. Dedicata, \({\bf 109}\) (2004), 165--173}], and [M. Atceken, Hacet. J. Math. Stat., \({\bf 44}\) (2015), 23--32]. %9 journal article %R 10.22436/jnsa.012.07.03 %U http://dx.doi.org/10.22436/jnsa.012.07.03 %P 440--449 %0 Journal Article %T Generalized Sasakian space forms %A P. Alegre %A D. E. Blair %A A. Carriazo %J Israel J. Math. %D 2004 %V 141 %F Alegre2004 %0 Journal Article %T Semi-invariant warped product submanifolds of almost contact manifolds %A F. R. Al-Solamy %A M. A. Khan %J J. Inequal. Appl. %D 2012 %V 2012 %F Al-Solamy2012 %0 Journal Article %T Contact CR-warped product submanifolds in Kenmotsu space forms %A K. Arslan %A R. Ezentas %A I. Mihai %A C. Murathan %J J. Korean Math. Soc. %D 2005 %V 42 %F Arslan2005 %0 Journal Article %T Contact CR-warped product submanifolds in cosymplectic space forms %A M. Atceken %J Collect. Math. %D 2011 %V 62 %F Atceken2011 %0 Journal Article %T Contact CR-warped product submanifolds in Kenmotsu space forms %A M. Atceken %J Bull. Iranian Math. Soc. %D 2013 %V 39 %F Atceken2013 %0 Journal Article %T Contact CR-warped product submanifolds in Sasakian space form %A M. Atceken %J Hacet. J. Math. Stat. %D 2015 %V 44 %F Atceken2015 %0 Journal Article %T Manifolds of Negative curvature %A R. L. Bishop %A B. O’Neill %J Trans. Amer. Math. Soc. %D 1965 %V 145 %F Bishop1965 %0 Book %T Contact manifolds in Riemannian Geometry %A D. E. Blair %D 1976 %I Springer-Verlag %C Berlin-New York %F Blair1976 %0 Journal Article %T Almost contact manifolds with Killing structure tensors II %A D. E. Blair %A D. K. Showers %J J. Differential Geometry %D 1974 %V 9 %F Blair1974 %0 Journal Article %T Nearly Sasakian structure %A D. E. Blair %A D. K. Showers %A K. Yano %J Kodai Math. Sem. Rep. %D 1976 %V 27 %F Blair1976 %0 Journal Article %T CR-submanifolds of a Kaehler manifold I %A B.-Y. Chen %J J. Differential Geom. %D 1981 %V 16 %F Chen1981 %0 Journal Article %T Geometry of warped product CR-submanifolds in Kaehler manifolds I %A B.-Y. Chen %J Monatsh Math. %D 2001 %V 133 %F Chen2001 %0 Book %T Pseudo-Riemannian Geometry, \(\delta\)-invariants and Applications %A B.-Y. Chen %D 2011 %I World Scientific Publishing Co. Pte. Ltd. %C Hackensack %F Chen2011 %0 Journal Article %T A survey on geometry of warped product submanifolds %A B.-Y. Chen %J arXiv %D 2013 %V 2013 %F Chen2013 %0 Journal Article %T Contact CR-warped product submanifolds in Sasakian manifolds %A I. Hasegawa %A I. Mihai %J Geom. Dedicata %D 2003 %V 102 %F Hasegawa2003 %0 Journal Article %T Warped products and black holes %A S.-T. Hong %J Nuovo Cimento Soc. Ital. Fis. B %D 2005 %V 120 %F Hong2005 %0 Journal Article %T Class of almost contact Riemannian manifolds %A K. Kenmotsu %J Tohoku Math. J. %D 1972 %V (2), 24 %F Kenmotsu1972 %0 Journal Article %T CR-warped product submanifolds of a generalized complex space form %A M. A. Khan %A A. A. Ishan %J Cogent Math. %D 2017 %V 4 %F Khan2017 %0 Journal Article %T Semi-invariant warped product submanifolds of cosymplectic manifolds %A M. A. Khan %A S. Uddin %A R. Sachdeva %J J. Inequal. Appl. %D 2012 %V 2012 %F Khan2012 %0 Journal Article %T Submanifolds of cosymplectic manifolds %A G. D. Ludden %J J. Differential Geometry %D 1970 %V 4 %F Ludden1970 %0 Journal Article %T Contact CR-warped product submanifolds in Sasakain space forms %A I. Mihai %J Geom. Dedicata %D 2004 %V 109 %F Mihai 2004 %0 Journal Article %T Warped product contact CR-submanifolds of Sasakian space forms %A M.-I. Munteanu %J Pubi. Math. Debrecen %D 2005 %V 66 %F Munteanu2005