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 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 Geometry of linear and angular momenta of N-particles in the Riemannian space forms and de Sitter space

2014 ◽  
Vol 86 ◽  
pp. 284-295
Author(s):  
Tetsuya Taniguchi ◽  
Seiichi Udagawa
Keyword(s):  
Riemannian Space ◽  
De Sitter Space ◽  
De Sitter ◽  
Space Forms ◽  
Angular Momenta ◽  
Riemannian Space Forms

scholarly journals Mode-sum construction of the two-point functions for the Stueckelberg vector fields in the Poincaré patch of de Sitter space

2014 ◽  
Vol 55 (6) ◽  
pp. 062301 ◽  
Author(s):  
Markus B. Fröb ◽  
Atsushi Higuchi
Keyword(s):  
Vector Fields ◽  
De Sitter Space ◽  
De Sitter

scholarly journals de Sitter symmetries and inflationary scalar-vector models

2016 ◽  
Vol 21 (3) ◽  
pp. 219 ◽  
Author(s):  
Cesar Alonso Valenzuela Toledo ◽  
Juan Beltrán Almeida ◽  
Josue Motoa-Manzano
Keyword(s):  
Field Theory ◽  
Euclidean Space ◽  
Correlation Functions ◽  
Vector Fields ◽  
Conformal Symmetry ◽  
De Sitter Space ◽  
Dual Theory ◽  
De Sitter ◽  
Curvature Perturbation ◽  
Scalar And Vector Fields

<div class="page" title="Page 1"><div class="section"><div class="layoutArea"><div class="column"><p><span>In this paper, we study the correspondence between a field theory in de Sitter space in D-dimensions and a dual conformal feld theory in a euclidean space in (D - 1)-dimensions. In particular, we investigate the form in which this correspondence is established for a system of interacting scalar and a vector fields propagating in de Sitter space. We analyze some necessary (but not sucient) conditions for which conformal symmetry is preserved in the dual theory in (D - 1)-dimensions, making possible the establishment of the correspondence. The discussion that we address in this paper is framed on the context of <em>inationary cosmology</em>. Thusly, the results obtained here pose some relevant possibilities of application to the calculation of the fields’s correlation functions and of the <em>primordial curvature perturbation</em> \zeta, in inationary models including coupled scalar and vector fields.</span></p></div></div></div></div>

scholarly journals Biharmonic Hypersurfaces in Pseudo-Riemannian Space Forms with at Most Two Distinct Principal Curvatures

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Chao Yang ◽  
Jiancheng Liu
Keyword(s):  
Euclidean Space ◽  
Mean Curvature ◽  
Riemannian Space ◽  
Constant Mean Curvature ◽  
Space Form ◽  
De Sitter Space ◽  
De Sitter ◽  
Principal Curvatures ◽  
Space Forms ◽  
Riemannian Space Forms

In this paper, we show that biharmonic hypersurfaces with at most two distinct principal curvatures in pseudo-Riemannian space form Nsn+1c with constant sectional curvature c and index s have constant mean curvature. Furthermore, we find that such biharmonic hypersurfaces Mr2k−1 in even-dimensional pseudo-Euclidean space Es2k, Ms−12k−1 in even-dimensional de Sitter space Ss2kcc>0, and Ms2k−1 in even-dimensional anti-de Sitter space ℍs2kcc<0 are minimal.

Propagators for massive vector fields in anti‐de Sitter space‐time using Stueckelberg’s Lagrangian

1987 ◽  
Vol 28 (5) ◽  
pp. 1023-1029 ◽  
Author(s):  
H. Janssen ◽  
C. Dullemond
Keyword(s):  
Vector Fields ◽  
De Sitter Space ◽  
Space Time ◽  
De Sitter ◽  
Massive Vector

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 Twisted submanifolds of $${\mathbb {R}}^n$$

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Gaetano Fiore ◽  
Thomas Weber
Keyword(s):  
Level Sets ◽  
Vector Fields ◽  
General Procedure ◽  
Killing Vector ◽  
Tangent Vector ◽  
De Sitter ◽  
Killing Vector Fields ◽  
Gauss Theorem ◽  
Levi Civita Connection ◽  
Algebraic Manifolds

AbstractWe propose a general procedure to construct noncommutative deformations of an embedded submanifold M of $${\mathbb {R}}^n$$ R n determined by a set of smooth equations $$f^a(x)=0$$ f a ( x ) = 0 . We use the framework of Drinfel’d twist deformation of differential geometry of Aschieri et al. (Class Quantum Gravity 23:1883, 2006); the commutative pointwise product is replaced by a (generally noncommutative) $$\star $$ ⋆ -product determined by a Drinfel’d twist. The twists we employ are based on the Lie algebra $$\Xi _t$$ Ξ t of vector fields that are tangent to all the submanifolds that are level sets of the $$f^a$$ f a (tangent infinitesimal diffeomorphisms); the twisted Cartan calculus is automatically equivariant under twisted $$\Xi _t$$ Ξ t . We can consistently project a connection from the twisted $${\mathbb {R}}^n$$ R n to the twisted M if the twist is based on a suitable Lie subalgebra $${\mathfrak {e}}\subset \Xi _t$$ e ⊂ Ξ t . If we endow $${\mathbb {R}}^n$$ R n with a metric, then twisting and projecting to the normal and tangent vector fields commute, and we can project the Levi–Civita connection consistently to the twisted M, provided the twist is based on the Lie subalgebra $${\mathfrak {k}}\subset {\mathfrak {e}}$$ k ⊂ e of the Killing vector fields of the metric; a twisted Gauss theorem follows, in particular. Twisted algebraic manifolds can be characterized in terms of generators and $$\star $$ ⋆ -polynomial relations. We present in some detail twisted cylinders embedded in twisted Euclidean $${\mathbb {R}}^3$$ R 3 and twisted hyperboloids embedded in twisted Minkowski $${\mathbb {R}}^3$$ R 3 [these are twisted (anti-)de Sitter spaces $$dS_2,AdS_2$$ d S 2 , A d S 2 ].

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