TY - JOUR AU - Ishan, Amira A. AU - Khan, Meraj Ali PY - 2019 TI - Contact CR-warped product submanifolds of a generalized Sasakian space form admitting a nearly Sasakian structure JO - Journal of Nonlinear Sciences and Applications SP - 440--449 VL - 12 IS - 7 AB - 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]. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.012.07.03 DO - 10.22436/jnsa.012.07.03 ID - Ishan2019 ER - TY - JOUR TI - Generalized Sasakian space forms AU - P. Alegre AU - D. E. Blair AU - A. Carriazo JO - Israel J. Math. PY - 2004 DA - 2004// VL - 141 ID - Alegre2004 ER - TY - JOUR TI - Semi-invariant warped product submanifolds of almost contact manifolds AU - F. R. Al-Solamy AU - M. A. Khan JO - J. Inequal. Appl. PY - 2012 DA - 2012// VL - 2012 ID - Al-Solamy2012 ER - TY - JOUR TI - Contact CR-warped product submanifolds in Kenmotsu space forms AU - K. Arslan AU - R. Ezentas AU - I. Mihai AU - C. Murathan JO - J. Korean Math. Soc. PY - 2005 DA - 2005// VL - 42 ID - Arslan2005 ER - TY - JOUR TI - Contact CR-warped product submanifolds in cosymplectic space forms AU - M. Atceken JO - Collect. Math. PY - 2011 DA - 2011// VL - 62 ID - Atceken2011 ER - TY - JOUR TI - Contact CR-warped product submanifolds in Kenmotsu space forms AU - M. Atceken JO - Bull. Iranian Math. Soc. PY - 2013 DA - 2013// VL - 39 ID - Atceken2013 ER - TY - JOUR TI - Contact CR-warped product submanifolds in Sasakian space form AU - M. Atceken JO - Hacet. J. Math. Stat. PY - 2015 DA - 2015// VL - 44 ID - Atceken2015 ER - TY - JOUR TI - Manifolds of Negative curvature AU - R. L. Bishop AU - B. O’Neill JO - Trans. Amer. Math. Soc. PY - 1965 DA - 1965// VL - 145 ID - Bishop1965 ER - TY - BOOK TI - Contact manifolds in Riemannian Geometry AU - D. E. Blair PB - Springer-Verlag PY - 1976 DA - 1976// CY - Berlin-New York ID - Blair1976 ER - TY - JOUR TI - Almost contact manifolds with Killing structure tensors II AU - D. E. Blair AU - D. K. Showers JO - J. Differential Geometry PY - 1974 DA - 1974// VL - 9 ID - Blair1974 ER - TY - JOUR TI - Nearly Sasakian structure AU - D. E. Blair AU - D. K. Showers AU - K. Yano JO - Kodai Math. Sem. Rep. PY - 1976 DA - 1976// VL - 27 ID - Blair1976 ER - TY - JOUR TI - CR-submanifolds of a Kaehler manifold I AU - B.-Y. Chen JO - J. Differential Geom. PY - 1981 DA - 1981// VL - 16 ID - Chen1981 ER - TY - JOUR TI - Geometry of warped product CR-submanifolds in Kaehler manifolds I AU - B.-Y. Chen JO - Monatsh Math. PY - 2001 DA - 2001// VL - 133 ID - Chen2001 ER - TY - BOOK TI - Pseudo-Riemannian Geometry, \(\delta\)-invariants and Applications AU - B.-Y. Chen PB - World Scientific Publishing Co. Pte. Ltd. PY - 2011 DA - 2011// CY - Hackensack ID - Chen2011 ER - TY - JOUR TI - A survey on geometry of warped product submanifolds AU - B.-Y. Chen JO - arXiv PY - 2013 DA - 2013// VL - 2013 ID - Chen2013 ER - TY - JOUR TI - Contact CR-warped product submanifolds in Sasakian manifolds AU - I. Hasegawa AU - I. Mihai JO - Geom. Dedicata PY - 2003 DA - 2003// VL - 102 ID - Hasegawa2003 ER - TY - JOUR TI - Warped products and black holes AU - S.-T. Hong JO - Nuovo Cimento Soc. Ital. Fis. B PY - 2005 DA - 2005// VL - 120 ID - Hong2005 ER - TY - JOUR TI - Class of almost contact Riemannian manifolds AU - K. Kenmotsu JO - Tohoku Math. J. PY - 1972 DA - 1972// VL - (2), 24 ID - Kenmotsu1972 ER - TY - JOUR TI - CR-warped product submanifolds of a generalized complex space form AU - M. A. Khan AU - A. A. Ishan JO - Cogent Math. PY - 2017 DA - 2017// VL - 4 ID - Khan2017 ER - TY - JOUR TI - Semi-invariant warped product submanifolds of cosymplectic manifolds AU - M. A. Khan AU - S. Uddin AU - R. Sachdeva JO - J. Inequal. Appl. PY - 2012 DA - 2012// VL - 2012 ID - Khan2012 ER - TY - JOUR TI - Submanifolds of cosymplectic manifolds AU - G. D. Ludden JO - J. Differential Geometry PY - 1970 DA - 1970// VL - 4 ID - Ludden1970 ER - TY - JOUR TI - Contact CR-warped product submanifolds in Sasakain space forms AU - I. Mihai JO - Geom. Dedicata PY - 2004 DA - 2004// VL - 109 ID - Mihai 2004 ER - TY - JOUR TI - Warped product contact CR-submanifolds of Sasakian space forms AU - M.-I. Munteanu JO - Pubi. Math. Debrecen PY - 2005 DA - 2005// VL - 66 ID - Munteanu2005 ER -