A General Inequality for CR-Warped Products in Generalized Sasakian Space Form and Its Applications

In the present paper, by considering the Gauss equation in place of the Codazzi equation, we derive new optimal inequality for the second fundamental form of CR-warped product submanifolds into a generalized Sasakian space form. Moreover, the inequality generalizes some inequalities for various ambient space forms.

[1]  R. Bishop,et al.  Manifolds of negative curvature , 1969 .

[2]  S. Dirik On some geometric properties of CR-submanifolds of a Sasakian manifold , 2020 .

[3]  Meraj Ali Khan,et al.  Ricci curvature of contact CR-warped product submanifolds in generalized Sasakian space forms admitting nearly Sasakian structure , 2021, AIMS Mathematics.

[4]  Yanlin Li,et al.  Lightlike tangent developables in de Sitter 3-space , 2021, Journal of Geometry and Physics.

[5]  Yanlin Li,et al.  Tangent developables and Darboux developables of framed curves , 2020 .

[6]  Sharief Deshmukh Trans-Sasakian Manifolds Homothetic to Sasakian Manifolds , 2016 .

[7]  Jianxun He,et al.  Some Results for the Two-Sided Quaternionic Gabor Fourier Transform and Quaternionic Gabor Frame Operator , 2020, Advances in Applied Clifford Algebras.

[8]  Alfonso Carriazo,et al.  Generalized Sasakian-space-forms , 2004 .

[9]  CONTACT CR-WARPED PRODUCT SUBMANIFOLDS OF NEARLY TRANS-SASAKIAN MANIFOLDS , 2013 .

[10]  I. Mihai Contact CR-Warped Product Submanifolds in Sasakian Space Forms , 2004 .

[11]  Contact CR-warped product submanifolds of generalized Sasakian space forms admitting Ricci soliton , 2019 .

[12]  L. Piscoran,et al.  Geometric classification of warped products isometrically immersed into Sasakian space forms , 2018, Mathematische Nachrichten.

[13]  Ricci curvature on warped product submanifolds of Sasakian-space-forms , 2020 .

[14]  Geometry of warped product pointwise semi-slant submanifolds of cosymplectic manifolds and its applications , 2017 .

[15]  Warped Product Pointwise Semi Slant Submanifolds of Sasakian Space Forms and their Applications , 2020 .

[16]  Characterization of warped product submanifolds in Kenmotsu manifolds , 2015 .

[17]  Chen type inequality for warped product immersions in cosymplectic space forms , 2016 .

[18]  Geometry of warped product immersions of Kenmotsu space forms and its applications to slant immersions , 2017 .

[19]  Yushu Zhu,et al.  Singularities and dualities of pedal curves in pseudo-hyperbolic and de Sitter space , 2020 .