scholarly journals The Smarandache Curves onS12and Its Duality onH02

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Atakan Tuğkan Yakut ◽  
Murat Savaş ◽  
Tuğba Tamirci
Keyword(s):  
Hyperbolic Space ◽  
De Sitter Space ◽  
Hyperbolic Spaces ◽  
De Sitter

We introduce special Smarandache curves based on Sabban frame onS12and we investigate geodesic curvatures of Smarandache curves on de Sitter and hyperbolic spaces. The existence of duality between Smarandache curves on de Sitter space and Smarandache curves on hyperbolic space is shown. Furthermore, we give examples of our main results.

scholarly journals SUBMANIFOLDS OF EUCLIDEAN SPACES SATISFYING $\Delta H =AH$

1995 ◽  
Vol 25 (1) ◽  
pp. 71-81
Author(s):  
BANG-YEN CHEN
Keyword(s):  
General Condition ◽  
Mean Curvature ◽  
Curvature Vector ◽  
De Sitter Space ◽  
Hyperbolic Spaces ◽  
Mean Curvature Vector ◽  
De Sitter ◽  
Euclidean Spaces

In [5] the author initiated the study of submanifolds whose mean curvature vector $H$ satisfying the condition $\Delta H =\lambda H$ for some constant $\lambda$ and proved that such submanifolds are either biharmonic or of 1-type or of null 2-type. Submanifolds of hyperbolic spaces and of de Sitter space-times satisfy this condition have been investigated and classified in [6,7]. In this article, we study submanifolds of $E^m$ whose mean curvature vector $H$ satisfies a more general condition; namely, $\Delta H =AH$ for some $m \times m$ matrix $A$.

scholarly journals Darboux Associated Curves of a Null Curve on Pseudo-Riemannian Space Forms

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 395
Author(s):  
Jinhua Qian ◽  
Xueshan Fu ◽  
Seoung Dal Jung
Keyword(s):  
Hyperbolic Space ◽  
Riemannian Space ◽  
De Sitter Space ◽  
De Sitter ◽  
Space Forms ◽  
Null Curve ◽  
Riemannian Space Forms ◽  
Relationship Of ◽  
The Relationship

In this work, the Darboux associated curves of a null curve on pseudo-Riemannian space forms, i.e., de-Sitter space, hyperbolic space and a light-like cone in Minkowski 3-space are defined. The relationships of such partner curves are revealed including the relationship of their Frenet frames and the curvatures. Furthermore, the Darboux associated curves of k-type null helices are characterized and the conclusion that a null curve and its self-associated curve share the same Darboux associated curve is obtained.

scholarly journals Normal Partner Curves of a Pseudo Null Curve on Dual Space Forms

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 919
Author(s):  
Jinhua Qian ◽  
Xueqian Tian ◽  
Young Ho Kim
Keyword(s):  
Hyperbolic Space ◽  
Dual Space ◽  
Vector Fields ◽  
Tangent Vector ◽  
De Sitter Space ◽  
Normal Curve ◽  
De Sitter ◽  
Space Forms ◽  
Null Curve

In this work, a kind of normal partner curves of a pseudo null curve on dual space forms is defined and studied. The Frenet frames and curvatures of a pseudo null curve and its associate normal curve on de-Sitter space, its associate normal curve on hyperbolic space, are related by some particular function and the angles between their tangent vector fields, respectively. Meanwhile, the relationships between the normal partner curves of a pseudo null curve are revealed. Last but not least, some examples are given and their graphs are plotted by the aid of a software programme.

scholarly journals The Subelliptic Heat Kernel of the Octonionic Anti-De Sitter Fibration

2021 ◽  
Author(s):  
Fabrice Baudoin ◽  
◽  
Gunhee Cho ◽  
Keyword(s):  
Heat Kernel ◽  
Hyperbolic Space ◽  
De Sitter Space ◽  
Integral Representations ◽  
De Sitter

In this note, we study the sub-Laplacian of the 15-dimensional octonionic anti-de Sitter space which is obtained by lifting with respect to the anti-de Sitter fibration the Laplacian of the octonionic hyperbolic space OH<sup>1</sup>. We also obtain two integral representations for the corresponding subelliptic heat kernel.

scholarly journals Compact Spacelike Hypersurfaces with Constant Mean Curvature in the Antide Sitter Space

2009 ◽  
Vol 2009 ◽  
pp. 1-12
Author(s):  
Henrique F. de Lima ◽  
Joseilson R. de Lima
Keyword(s):  
Hyperbolic Space ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Spacelike Hypersurface ◽  
De Sitter Space ◽  
De Sitter ◽  
Height Estimate ◽  
Spacelike Hypersurfaces ◽  
Hyperbolic Domains

We obtain a height estimate concerning to a compact spacelike hypersurfaceΣnimmersed with constant mean curvatureHin the anti-de Sitter spaceℍ1n+1, when its boundary∂Σis contained into an umbilical spacelike hypersurface of this spacetime which is isometric to the hyperbolic spaceℍn. Our estimate depends only on the value ofHand on the geometry of∂Σ.As applications of our estimate, we obtain a characterization of hyperbolic domains ofℍ1n+1and nonexistence results in connection with such types of hypersurfaces.

Convergence theorems for total asymptotically nonexpansive single-valued and quasi nonexpansive multi-valued mappings in hyperbolic spaces

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Preeyalak Chuadchawna ◽  
Ali Farajzadeh ◽  
Anchalee Kaewcharoen
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Hyperbolic Space ◽  
Hyperbolic Spaces ◽  
Iterative Sequence ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive ◽  
Uniformly Convex Hyperbolic Space

Abstract In this paper, we discuss the Δ-convergence and strong convergence for the iterative sequence generated by the proposed scheme to approximate a common fixed point of a total asymptotically nonexpansive single-valued mapping and a quasi nonexpansive multi-valued mapping in a complete uniformly convex hyperbolic space. Finally, by giving an example, we illustrate our result.

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