Spacelike Möbius Hypersurfaces in Four Dimensional Lorentzian Space Form

2019 ◽  
Vol 35 (4) ◽  
pp. 519-536 ◽  
Author(s):  
Yan Bin Lin ◽  
Ying Lü ◽  
Chang Ping Wang
Keyword(s):  
Space Form ◽  
Lorentzian Space

Chen-like inequalities on null hypersurfaces with closed rigging of a Lorentzian manifold

2021 ◽  
pp. 2150125
Author(s):  
Amrinder Pal Singh ◽  
Cyriaque Atindogbe ◽  
Rakesh Kumar ◽  
Varun Jain
Keyword(s):  
Scalar Curvature ◽  
Space Form ◽  
Lorentzian Manifold ◽  
Null Hypersurface ◽  
Lorentzian Space ◽  
Null Hypersurfaces

We study null hypersurfaces of a Lorentzian manifold with a closed rigging for the hypersurface. We derive inequalities involving Ricci tensors, scalar curvature, squared mean curvatures for a null hypersurface with a closed rigging of a Lorentzian space form and for a screen homothetic null hypersurface of a Lorentzian manifold. We also establish a generalized Chen–Ricci inequality for a screen homothetic null hypersurface of a Lorentzian manifold with a closed rigging for the hypersurface.

scholarly journals Hypersurface Constrained Elasticae in Lorentzian Space Forms

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Óscar J. Garay ◽  
Álvaro Pámpano ◽  
Changhwa Woo
Keyword(s):  
Space Form ◽  
Energy Functional ◽  
Bending Energy ◽  
Space Forms ◽  
Lorentzian Space ◽  
Totally Geodesic ◽  
Critical Curves ◽  
Different Types ◽  
Lorentzian Space Forms

We study geodesics in hypersurfaces of a Lorentzian space formM1n+1(c), which are critical curves of theM1n+1(c)-bending energy functional, for variations constrained to lie on the hypersurface. We characterize critical geodesics showing that they live fully immersed in a totally geodesicM13(c)and that they must be of three different types. Finally, we consider the classification of surfaces in the Minkowski 3-space foliated by critical geodesics.

scholarly journals Integrability aspects of the vortex filament equation for pseudo-null curves

2017 ◽  
Vol 14 (06) ◽  
pp. 1750090 ◽  
Author(s):  
José del Amor ◽  
Ángel Giménez ◽  
Pascual Lucas
Keyword(s):  
Space Form ◽  
Burgers Equation ◽  
Three Dimensional ◽  
Recursion Operator ◽  
Vortex Filament ◽  
Lorentzian Space ◽  
Null Curve ◽  
Vortex Filament Equation ◽  
Null Curves ◽  
The Relationship

An algebraic background in order to study the integrability properties of pseudo-null curve motions in a three-dimensional Lorentzian space form is developed. As an application, we delve into the relationship between the Burgers’ equation and the pseudo-null vortex filament equation. A recursion operator for the pseudo-null vortex filament equation is also provided.

scholarly journals Willmore spacelike submanifolds in an indefinite space form Nn+p q(c)

2017 ◽  
Vol 102 (116) ◽  
pp. 175-193
Author(s):  
Shichang Shu ◽  
Junfeng Chen
Keyword(s):  
Space Form ◽  
Second Fundamental Form ◽  
Integral Inequalities ◽  
Willmore Functional ◽  
Lorentzian Space ◽  
The Second Fundamental Form ◽  
Spacelike Submanifold ◽  
Spacelike Submanifolds ◽  
The Mean ◽  
Rigidity Theorems

Let Nn+p q(c) be an (n+p)-dimensional connected indefinite space form of index q(1 ? q ? p) and of constant curvature c. Denote by ? : M ? Nn+p q (c) the n-dimensional spacelike submanifold in Nn+p q (c), ? : M ? Nn+p q(c) is called a Willmore spacelike submanifold in Nn+p q(c) if it is a critical submanifold to the Willmore functional W(?) = ?q M ?n dv =?M (S-nH2)n/2 dv, where S and H denote the norm square of the second fundamental form and the mean curvature of M and ?2 = S ? nH2. If q = p, in [14], we proved some integral inequalities of Simons? type and rigidity theorems for n-dimensional Willmore spacelike submanifolds in a Lorentzian space form Nn+p q(c). In this paper, we continue to study this topic and prove some integral inequalities of Simons? type and rigidity theorems for n-dimensional Willmore spacelike submanifolds in an indefinite space form Nn+p q(c) (1 ? q ? p).

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