Classification of quasi-minimal slant surfaces in Lorentzian complex space forms

2008 ◽  
Vol 122 (4) ◽  
pp. 307-328 ◽  
Author(s):  
B. Y. Chen ◽  
I. Mihai
Keyword(s):  
Complex Space ◽  
Space Forms ◽  
Complex Space Forms

scholarly journals Existence and uniqueness of inhomogeneous ruled hypersurfaces with shape operator of constant norm in the complex hyperbolic space

2021 ◽  
pp. 2150049
Author(s):  
Miguel Domínguez-Vázquez ◽  
Olga Pérez-Barral
Keyword(s):  
Hyperbolic Space ◽  
Complex Space ◽  
Shape Operator ◽  
Complex Hyperbolic Space ◽  
Real Hypersurfaces ◽  
Space Forms ◽  
Nonflat Complex Space Forms ◽  
Ruled Real Hypersurfaces ◽  
Complex Space Forms

We complete the classification of ruled real hypersurfaces with shape operator of constant norm in nonflat complex space forms by showing the existence of a unique inhomogeneous example in the complex hyperbolic space.

scholarly journals Classification of δ(2,n− 2)-ideal Lagrangian submanifolds in n-dimensional complex space forms

2018 ◽  
Vol 458 (2) ◽  
pp. 1456-1485 ◽  
Author(s):  
Bang-Yen Chen ◽  
Franki Dillen ◽  
Joeri Van der Veken ◽  
Luc Vrancken
Keyword(s):  
Complex Space ◽  
Lagrangian Submanifolds ◽  
Space Forms ◽  
Complex Space Forms

REAL HYPERSURFACES OF NON-FLAT COMPLEX SPACE FORMS WITH GENERALIZED ξ-PARALLEL JACOBI STRUCTURE OPERATOR

2015 ◽  
Vol 58 (3) ◽  
pp. 677-687
Author(s):  
TH. THEOFANIDIS
Keyword(s):  
Tangent Space ◽  
Complex Space ◽  
Real Hypersurfaces ◽  
Space Forms ◽  
Jacobi Structure ◽  
Complex Space Forms ◽  
First Time

AbstractThe aim of the present paper is the classification of real hypersurfaces M equipped with the condition Al = lA, l = R(., ξ)ξ, restricted in a subspace of the tangent space TpM of M at a point p. This class is large and difficult to classify, therefore a second condition is imposed: (∇ξl)X = ω(X)ξ + ψ(X)lX, where ω(X), ψ(X) are 1-forms. The last condition is studied for the first time and is much weaker than ∇ξl = 0 which has been studied so far. The Jacobi Structure Operator satisfying this weaker condition can be called generalized ξ-parallel Jacobi Structure Operator.

Jacobi's elliptic functions and Lagrangian immersions

1996 ◽  
Vol 126 (4) ◽  
pp. 687-704 ◽  
Author(s):  
Bang-Yen Chen
Keyword(s):  
Complex Space ◽  
Lagrangian Submanifolds ◽  
Elliptic Functions ◽  
Complete Classification ◽  
Sharp Inequality ◽  
Space Forms ◽  
Nonflat Complex Space Forms ◽  
Basic Equality ◽  
Complex Space Forms

First, we establish a sharp inequality between the squared mean curvature and the scalar curvature for a Lagrangian submanifold in a nonflat complex-space-form. Then, by utilising the Jacobi's elliptic functions en and dn, we introduce three families of Lagrangian submanifolds and two exceptional Lagrangian submanifolds Fn, Ln in nonflat complex-space-forms which satisfy the equality case of the inequality. Finally, we obtain the complete classification of Lagrangian submanifolds in nonflat complex-space-forms which satisfy this basic equality.

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.

A Classification of Three-dimensional Real Hypersurfaces in Non-flat Complex Space Forms in Terms of their Generalized Tanaka–Webster Lie Derivative

2016 ◽  
Vol 59 (4) ◽  
pp. 813-823
Author(s):  
George Kaimakamis ◽  
Konstantina Panagiotidou ◽  
Juan de Dios Perez
Keyword(s):  
Vector Field ◽  
Complex Space ◽  
Space Form ◽  
Three Dimensional ◽  
Real Hypersurfaces ◽  
Lie Derivative ◽  
Space Forms ◽  
Levi Civita Connection ◽  
Complex Space Forms

AbstractOn a real hypersurface M in a non-flat complex space form there exist the Levi–Civita and the k-th generalized Tanaka–Webster connections. The aim of this paper is to study three dimensional real hypersurfaces in non-flat complex space forms, whose Lie derivative of the structure Jacobi operatorwith respect to the Levi–Civita connection coincides with the Lie derivative of it with respect to the k-th generalized Tanaka-Webster connection. The Lie derivatives are considered in direction of the structure vector field and in direction of any vector field orthogonal to the structure vector field.

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