scholarly journals PSEUDO-PARALLEL KAEHLERIAN SUBMANIFOLDS IN COMPLEX SPACE FORMS

2020 ◽  
pp. 321
Author(s):  
Ahmet Yildiz
Keyword(s):  
Sectional Curvature ◽  
Fundamental Form ◽  
Complex Space ◽  
Space Form ◽  
Dimensional Space ◽  
Second Fundamental Form ◽  
Holomorphic Sectional Curvature ◽  
Space Forms ◽  
Totally Geodesic ◽  
Complex Space Forms

Let $\tilde{M}^{m}(c)$ be a complex $m$-dimensional space form of holomorphic sectional curvature $c$ and $M^{n}$ be a complex $n$-dimensional Kaehlerian submanifold of $\tilde{M}^{m}(c).$ We prove that if $M^{n}$ is pseudo-parallel and $Ln-\frac{1}{2}(n+2)c\geqslant 0$ then $M$ $^{n}$ is totally geodesic. Also, we study Kaehlerian submanifolds of complex space form with recurrent second fundamental form.

scholarly journals Parallel submanifolds of complex space forms I

1983 ◽  
Vol 90 ◽  
pp. 85-117 ◽  
Author(s):  
Hiroo Naitoh
Keyword(s):  
Symmetric Space ◽  
Sectional Curvature ◽  
Complex Space ◽  
Space Form ◽  
Real Space ◽  
Hermitian Symmetric Space ◽  
Holomorphic Sectional Curvature ◽  
Space Forms ◽  
Simply Connected ◽  
Complex Space Forms

Complete parallel submanifolds of a real space form of constant sectional curvature k have been completely classified by Ferus [3] when k ≧ 0, and by Takeuchi [19] when k < 0. A complex space form is by definition a 2n-dimensional simply connected Hermitian symmetric space of constant holomorphic sectional curvature c and will be denoted by (c).

On 4-dimensional generalized complex space forms

1999 ◽  
Vol 66 (3) ◽  
pp. 379-387 ◽  
Author(s):  
Un Kyu Kim
Keyword(s):  
Sectional Curvature ◽  
Complex Space ◽  
Hermitian Manifold ◽  
Holomorphic Sectional Curvature ◽  
Space Forms ◽  
Generalized Complex ◽  
Complex Forms ◽  
Complex Space Forms

AbstractWe characterize four-dimensional generalized complex forms and construct an Einstein and weakly *-Einstein Hermitian manifold with pointwise constant holomorphic sectional curvature which is not globally constant.

Biwarped product submanifolds of complex space forms

2019 ◽  
Vol 16 (05) ◽  
pp. 1950072 ◽  
Author(s):  
Meraj Ali Khan ◽  
Kamran Khan
Keyword(s):  
Fundamental Form ◽  
Warped Product ◽  
Complex Space ◽  
Second Fundamental Form ◽  
Warping Function ◽  
Space Forms ◽  
Kaehler Manifolds ◽  
The Second Fundamental Form ◽  
Complex Space Forms ◽  
Special Case

The class of biwarped product manifolds is a generalized class of product manifolds and a special case of multiply warped product manifolds. In this paper, biwarped product submanifolds of the type [Formula: see text] embedded in the complex space forms are studied. Some characterizing inequalities for the existence of such type of submanifolds are derived. Moreover, we also estimate the squared norm of the second fundamental form in terms of the warping function and the slant function. This inequality generalizes the result obtained by Chen in [B. Y. Chen, Geometry of warped product CR-submanifolds in Kaehler manifolds I, Monatsh. Math. 133 (2001) 177–195]. By the application of derived inequality, we compute the Dirichlet energies of the warping functions involved. A nontrivial example of these warped product submanifolds is provided.

COMPLETE CLASSIFICATION OF PARALLEL LORENTZIAN SURFACES IN LORENTZIAN COMPLEX SPACE FORMS

2010 ◽  
Vol 21 (05) ◽  
pp. 665-686 ◽  
Author(s):  
BANG-YEN CHEN ◽  
FRANKI DILLEN ◽  
JOERI VAN DER VEKEN
Keyword(s):  
Riemannian Manifold ◽  
Fundamental Form ◽  
Complex Space ◽  
Complete Classification ◽  
Second Fundamental Form ◽  
Space Forms ◽  
Complex Dimension ◽  
Point To Point ◽  
Complex Space Forms

A surface of a pseudo-Riemannian manifold is called parallel if its second fundamental form is parallel with respect to the Van der Waerden–Bortolotti connection. Such surfaces are fundamental since the extrinsic invariants of the surfaces do no change from point to point. In this article, we completely classify parallel Lorentzian surfaces in Lorentzian complex space forms of complex dimension two.

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.

scholarly journals Strongly pseudo-convex CR space forms

2019 ◽  
Vol 6 (1) ◽  
pp. 279-293 ◽  
Author(s):  
Jong Taek Cho
Keyword(s):  
Sectional Curvature ◽  
Hyperbolic Space ◽  
Space Form ◽  
Contact Manifold ◽  
Holomorphic Sectional Curvature ◽  
Sphere Bundle ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Pseudo Convex ◽  
Unit Tangent Sphere Bundle

AbstractFor a contact manifold, we study a strongly pseudo-convex CR space form with constant holomorphic sectional curvature for the Tanaka-Webster connection. We prove that a strongly pseudo-convex CR space form M is weakly locally pseudo-Hermitian symmetric if and only if (i) dim M = 3, (ii) M is a Sasakian space form, or (iii) M is locally isometric to the unit tangent sphere bundle T1(𝔿n+1) of a hyperbolic space 𝔿n+1 of constant curvature −1.

scholarly journals Quasi-Einstein Hypersurfaces of Complex Space Forms

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Xiaomin Chen ◽  
Xuehui Cui
Keyword(s):  
Real Hypersurface ◽  
Complex Space ◽  
Space Form ◽  
Ricci Soliton ◽  
Complex Space Form ◽  
Einstein Metric ◽  
Space Forms ◽  
The Real ◽  
Complex Euclidean Space ◽  
Complex Space Forms

Based on a well-known fact that there are no Einstein hypersurfaces in a nonflat complex space form, in this article, we study the quasi-Einstein condition, which is a generalization of an Einstein metric, on the real hypersurface of a nonflat complex space form. For the real hypersurface with quasi-Einstein metric of a complex Euclidean space, we also give a classification. Since a gradient Ricci soliton is a special quasi-Einstein metric, our results improve some conclusions of Cho and Kimura.

The normalized Ricci flow and homology in Lagrangian submanifolds of generalized complex space forms

2020 ◽  
Vol 17 (06) ◽  
pp. 2050094 ◽  
Author(s):  
Fatemah Mofarreh ◽  
Akram Ali ◽  
Wan Ainun Mior Othman
Keyword(s):  
Fundamental Form ◽  
Ricci Flow ◽  
Complex Space ◽  
Space Form ◽  
Second Fundamental Form ◽  
Complex Space Form ◽  
Standard Sphere ◽  
The Second Fundamental Form ◽  
Generalized Complex ◽  
Normalized Ricci Flow

In this paper, we prove that a simply connected Lagrangian submanifold in the generalized complex space form is diffeomorphic to standard sphere [Formula: see text] and the normalized Ricci flow converges to a constant curvature metric, provided its squared norm of the second fundamental form satisfies some upper bound depending only on the squared norm of the mean curvature vector field, the constant sectional curvature, and the dimension of the Lagrangian immersion of the ambient space. Next, we conclude that stable currents do not exist and homology groups vanish in a compact real submanifold of the general complex space form, provided that the second fundamental form satisfies some extrinsic conditions. We show that our results improve some previous results.

Sign in / Sign up

Export Citation Format

Share Document