Warped product pointwise semi-slant submanifolds of the complex space forms

2019 ◽  
Vol 69 (1) ◽  
pp. 195-207
Author(s):  
Meraj Ali Khan
Keyword(s):  
Warped Product ◽  
Complex Space ◽  
Space Forms ◽  
Slant Submanifolds ◽  
Complex Space Forms

scholarly journals Geometric Mechanics on Warped Product Semi-Slant Submanifold of Generalized Complex Space Forms

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Yanlin Li ◽  
Ali H. Alkhaldi ◽  
Akram Ali
Keyword(s):  
Warped Product ◽  
Complex Space ◽  
Slant Submanifold ◽  
Codazzi Equation ◽  
Space Forms ◽  
Kaehler Manifolds ◽  
Slant Submanifolds ◽  
Generalized Complex ◽  
Complex Space Forms ◽  
Nearly Kaehler Manifold

In this study, we develop a general inequality for warped product semi-slant submanifolds of type M n = N T n 1 × f N ϑ n 2 in a nearly Kaehler manifold and generalized complex space forms using the Gauss equation instead of the Codazzi equation. There are several applications that can be developed from this. It is also described how to classify warped product semi-slant submanifolds that satisfy the equality cases of inequalities (determined using boundary conditions). Several results for connected, compact warped product semi-slant submanifolds of nearly Kaehler manifolds are obtained, and they are derived in the context of the Hamiltonian, Dirichlet energy function, gradient Ricci curvature, and nonzero eigenvalue of the Laplacian of the warping functions.

scholarly journals Chen Inequalities for Warped Product Pointwise Bi-Slant Submanifolds of Complex Space Forms and Its Applications

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 200
Author(s):  
Akram Ali ◽  
Ali Alkhaldi
Keyword(s):  
Mean Curvature ◽  
Warped Product ◽  
Complex Space ◽  
Holomorphic Sectional Curvature ◽  
Warping Function ◽  
Space Forms ◽  
Slant Submanifolds ◽  
The Mean ◽  
Complex Space Forms ◽  
Inequality Theorem

In this paper, by using new-concept pointwise bi-slant immersions, we derive a fundamental inequality theorem for the squared norm of the mean curvature via isometric warped-product pointwise bi-slant immersions into complex space forms, involving the constant holomorphic sectional curvature c, the Laplacian of the well-defined warping function, the squared norm of the warping function, and pointwise slant functions. Some applications are also given.

Ricci curvature on warped product submanifolds of complex space forms and its applications

2019 ◽  
Vol 16 (09) ◽  
pp. 1950142 ◽  
Author(s):  
Akram Ali ◽  
Pişcoran Laurian-Ioan ◽  
Ali H. Alkhaldi ◽  
Lamia Saeed Alqahtani
Keyword(s):  
Ricci Curvature ◽  
Warped Product ◽  
Complex Space ◽  
Shape Operator ◽  
Isometric Immersions ◽  
Differential Function ◽  
Space Forms ◽  
Slant Submanifolds ◽  
Arbitrary Codimension ◽  
Complex Space Forms

The upper bound of Ricci curvature conjecture, also known as Chen-Ricci conjecture, was formulated by Chen [B. Y. Chen, Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimension, Glasgow Math. J. 41 (1999) 33–41] and modified by Tripathi [M. M. Tripathi, Improved Chen–Ricci inequality for curvature-like tensors and its applications, Diff. Geom. Appl. 29 (2011) 685–698]. In this paper, first, we define partially minimal isometric immersion of warped product manifolds. Then, we derive a fundamental theorem for Ricci curvature via partially minimal isometric immersions from a warped product pointwise bi-slant submanifolds into complex space forms. Some applications are constructed in terms of Dirichlet energy function, Hamiltonian, Lagrangian and Hessian tensor due to appearance of the positive differential function in the inequality.

scholarly journals Analysis of Obata’s Differential Equations on Pointwise Semislant Warped Product Submanifolds of Complex Space Forms via Ricci Curvature

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Amira A. Ishan
Keyword(s):  
Differential Equations ◽  
Ricci Curvature ◽  
Warped Product ◽  
Complex Space ◽  
Space Forms ◽  
Geometric Conditions ◽  
Isometric To A Sphere ◽  
Complex Space Forms

The present paper studies the applications of Obata’s differential equations on the Ricci curvature of the pointwise semislant warped product submanifolds. More precisely, by analyzing Obata’s differential equations on pointwise semislant warped product submanifolds, we demonstrate that, under certain conditions, the base of these submanifolds is isometric to a sphere. We also look at the effects of certain differential equations on pointwise semislant warped product submanifolds and show that the base is isometric to a special type of warped product under some geometric conditions.

scholarly journals The First Fundamental Equation and Generalized Wintgen-Type Inequalities for Submanifolds in Generalized Space Forms

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1151 ◽  
Author(s):  
Mohd. Aquib ◽  
Michel Nguiffo Boyom ◽  
Mohammad Hasan Shahid ◽  
Gabriel-Eduard Vîlcu
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Fundamental Equation ◽  
Type Inequality ◽  
Lagrangian Submanifold ◽  
Space Forms ◽  
Slant Submanifolds ◽  
Sasakian Space Forms ◽  
Generalized Complex ◽  
Complex Space Forms

In this work, we first derive a generalized Wintgen type inequality for a Lagrangian submanifold in a generalized complex space form. Further, we extend this inequality to the case of bi-slant submanifolds in generalized complex and generalized Sasakian space forms and derive some applications in various slant cases. Finally, we obtain obstructions to the existence of non-flat generalized complex space forms and non-flat generalized Sasakian space forms in terms of dimension of the vector space of solutions to the first fundamental equation on such spaces.

Some inequalities of slant submanifolds in generalized complex space forms

2005 ◽  
Vol 36 (3) ◽  
pp. 223-229 ◽  
Author(s):  
Aimin Song ◽  
Ximin Liu
Keyword(s):  
Scalar Curvature ◽  
Ricci Curvature ◽  
Mean Curvature ◽  
Complex Space ◽  
Space Forms ◽  
Slant Submanifolds ◽  
Generalized Complex ◽  
Complex Space Forms ◽  
Normalized Scalar Curvature

In this paper, we obtain an inequality about Ricci curvature and squared mean curvature of slant submanifolds in generalized complex space forms. We also obtain an inequality about the squared mean curvature and the normalized scalar curvature of slant submanifolds in generalized coplex space forms.

scholarly journals AN IMPROVED CHEN-RICCI INEQUALITY FOR KAEHLERIAN SLANT SUBMANIFOLDS IN COMPLEX SPACE FORMS

2012 ◽  
Vol 16 (2) ◽  
pp. 761-770 ◽  
Author(s):  
Adela Mihai ◽  
Ioana N. Rădulescu
Keyword(s):  
Complex Space ◽  
Space Forms ◽  
Slant Submanifolds ◽  
Complex Space Forms

scholarly journals Ricci tensor of slant submanifolds in complex space forms

2003 ◽  
Vol 26 (1) ◽  
pp. 85-94 ◽  
Author(s):  
Koji Matsumoto ◽  
Ion Mihai ◽  
Yoshihiko Tazawa
Keyword(s):  
Ricci Tensor ◽  
Complex Space ◽  
Space Forms ◽  
Slant Submanifolds ◽  
Complex Space Forms

scholarly journals Characterization of Skew CR-Warped Product Submanifolds in Complex Space Forms via Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Ibrahim Al-Dayel ◽  
Meraj Ali Khan
Keyword(s):  
Euclidean Space ◽  
Differential Equations ◽  
Warped Product ◽  
Complex Space ◽  
Space Form ◽  
Space Forms ◽  
Geometric Conditions ◽  
Complex Space Forms ◽  
The Impact

Recently, we have obtained Ricci curvature inequalities for skew CR-warped product submanifolds in the framework of complex space form. By the application of Bochner’s formula on these inequalities, we show that, under certain conditions, the base of these submanifolds is isometric to the Euclidean space. Furthermore, we study the impact of some differential equations on skew CR-warped product submanifolds and prove that, under some geometric conditions, the base is isometric to a special type of warped product.

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