A New Characterization of One Parameter Family of Surfaces by Inextensible Flows in De-Sitter 3-Space

2018 ◽  
Vol 7 (2) ◽  
pp. 251-256 ◽  
Author(s):  
Selçuk Baş ◽  
Talat Körpinar
Keyword(s):  
Parameter Family ◽  
De Sitter ◽  
Inextensible Flows

scholarly journals On new characterization of inextensible flows of space-like curves in de Sitter space

2016 ◽  
Vol 14 (1) ◽  
pp. 946-954 ◽  
Author(s):  
Mustafa Yeneroğlu
Keyword(s):  
De Sitter Space ◽  
De Sitter ◽  
Practical Applications ◽  
Inextensible Flows

AbstractElastica and inextensible flows of curves play an important role in practical applications. In this paper, we construct a new characterization of inextensible flows by using elastica in space. The inextensible flow is completely determined for any space-like curve in de Sitter space $\mathbb{S}_{1}^{3}$. Finally, we give some characterizations for curvatures of a space-like curve in de Sitter space $\mathbb{S}_{1}^{3}$.

scholarly journals Graviton propagator in a 2-parameter family of de Sitter breaking gauges

2019 ◽  
Vol 2019 (10) ◽  
Author(s):  
D. Glavan ◽  
S.P. Miao ◽  
T. Prokopec ◽  
R.P. Woodard
Keyword(s):  
Parameter Family ◽  
De Sitter ◽  
Graviton Propagator

scholarly journals Weingarten spacelike hypersurfaces in a de Sitter space

2012 ◽  
Vol 20 (1) ◽  
pp. 387-406
Author(s):  
Junfeng Chen ◽  
Shichang Shu
Keyword(s):  
De Sitter Space ◽  
De Sitter ◽  
Principal Curvatures ◽  
Riemannian Product ◽  
Spacelike Hypersurfaces ◽  
Hyperbolic Cylinder

Abstract We study some Weingarten spacelike hypersurfaces in a de Sitter space S1n+1 (1). If the Weingarten spacelike hypersurfaces have two distinct principal curvatures, we obtain two classification theorems which give some characterization of the Riemannian product Hk(1−coth2 ϱ)× Sn−k(1 − tanh2 ϱ), 1 < k < n − 1 in S1n+1(1), the hyperbolic cylinder H1(1 − coth2 ϱ) × Sn-1(1 − tanh2 ϱ) or spherical cylinder Hn−1(1 − coth2 ϱ) × S1(1 − tanh2 ϱ) in S1n+1 (1)

scholarly journals Characterization of inextensible flows of spacelike curves with sabban frame in S₁²

2013 ◽  
Vol 31 (2) ◽  
pp. 47 ◽  
Author(s):  
Mahmut Ergüt ◽  
Essin Turhan ◽  
Talat Körpınar
Keyword(s):  
Inextensible Flows

In this paper, we study inextensible flows of spacelike curves on S₁². We research inextensible flows of spacelike curves according to Sabban frame on S₁².

A topological criterion for group decompositions

1988 ◽  
Vol 103 (2) ◽  
pp. 285-298 ◽  
Author(s):  
J. Hebda ◽  
P. Moylan
Keyword(s):  
Asymptotic Properties ◽  
Cartesian Product ◽  
Conformal Field Theories ◽  
De Sitter ◽  
Group Representations ◽  
Conformal Field ◽  
Connected Subgroup ◽  
Closed Connected Subgroup ◽  
Necessary And Sufficient

AbstractGiven a connected Lie group G and a closed connected subgroup H of G we prove a necessary and sufficient condition that G decomposes into the Cartesian product of H with G/H is that a similar decomposition holds for the maximal compact subgroups of G and H. Our criterion is applied to the three series of groups for which G/H is SO0(p, q)/SO0(p, q − 1), SU(q + 1, q + 1)/S[U(q + 1, q) × U(1)], and SU(q + 1, q + 1)/SL(n, ℂ) ⋊ H(n) (p, q ≥ 1), and we list the values of p and q for which G ≅ H × G/H in each of the three cases. We describe certain decompositions for some of the groups. We show the usefulness of our criterion in obtaining characterization of the space of differentiable vectors for a unitary induced group representation, and, finally, we show by example of SU(2, 2), how the asymptotic properties of certain function spaces for induced group representations are readily obtained using our results. Our results should be of interest to those working in de Sitter and conformal field theories.

scholarly journals GEOMETRIC MODULAR ACTION AND SPACETIME SYMMETRY GROUPS

2000 ◽  
Vol 12 (04) ◽  
pp. 475-560 ◽  
Author(s):  
DETLEV BUCHHOLZ ◽  
OLAF DREYER ◽  
MARTIN FLORIG ◽  
STEPHEN J. SUMMERS
Keyword(s):  
Isometry Group ◽  
Three Dimensional ◽  
Algebraic Characterization ◽  
Symmetry Groups ◽  
De Sitter ◽  
Vacuum States ◽  
Point Transformations ◽  
Projective Representations ◽  
Modular Covariance

A condition of geometric modular action is proposed as a selection principle for physically interesting states on general space-times. This condition is naturally associated with transformation groups of partially ordered sets and provides these groups with projective representations. Under suitable additional conditions, these groups induce groups of point transformations on these space-times, which may be interpreted as symmetry groups. The consequences of this condition are studied in detail in application to two concrete space-times — four-dimensional Minkowski and three-dimensional de Sitter spaces — for which it is shown how this condition characterizes the states invariant under the respective isometry group. An intriguing new algebraic characterization of vacuum states is given. In addition, the logical relations between the condition proposed in this paper and the condition of modular covariance, widely used in the literature, are completely illuminated.

scholarly journals Characterization of (asymptotically) Kerr–de Sitter-like spacetimes at null infinity

2016 ◽  
Vol 33 (15) ◽  
pp. 155001 ◽  
Author(s):  
Marc Mars ◽  
Tim-Torben Paetz ◽  
José M M Senovilla ◽  
Walter Simon
Keyword(s):  
De Sitter ◽  
Null Infinity

scholarly journals Free data at spacelike $${\mathscr {I}}$$ and characterization of Kerr-de Sitter in all dimensions

2021 ◽  
Vol 81 (10) ◽  
Author(s):  
Marc Mars ◽  
Carlos Peón-Nieto
Keyword(s):  
Weyl Tensor ◽  
Universal Constant ◽  
Vacuum Field ◽  
De Sitter ◽  
Field Equations ◽  
Null Infinity ◽  
Conformal Flatness ◽  
Free Data ◽  
The Cauchy Problem

AbstractWe study the free data in the Fefferman–Graham expansion of asymptotically Einstein $$(n+1)$$ ( n + 1 ) -dimensional metrics with non-zero cosmological constant. We analyze the relation between the electric part of the rescaled Weyl tensor at $${\mathscr {I}}$$ I , D, and the free data at $${\mathscr {I}}$$ I , namely a certain traceless and transverse part of the n-th order coefficient of the expansion $$\mathring{g}_{(n)}$$ g ˚ ( n ) . In the case $$\Lambda <0$$ Λ < 0 and Lorentzian signature, it was known [23] that conformal flatness at $${\mathscr {I}}$$ I is sufficient for D and $$\mathring{g}_{(n)}$$ g ˚ ( n ) to agree up to a universal constant. We recover and extend this result to general signature and any sign of non-zero $$\Lambda $$ Λ . We then explore whether conformal flatness of $${\mathscr {I}}$$ I is also neceesary and link this to the validity of long-standing open conjecture that no non-trivial purely magnetic $$\Lambda $$ Λ -vacuum spacetimes exist. In the case of $${\mathscr {I}}$$ I non-conformally flat we determine a quantity constructed from an auxiliary metric which can be used to retrieve $$\mathring{g}_{(n)}$$ g ˚ ( n ) from the (now singular) electric part of the Weyl tensor. We then concentrate in the $$\Lambda >0$$ Λ > 0 case where the Cauchy problem at $${\mathscr {I}}$$ I of the Einstein vacuum field equations is known to be well-posed when the data at $${\mathscr {I}}$$ I are analytic or when the spacetime has even dimension. We establish a necessary and sufficient condition for analytic data at $${\mathscr {I}}$$ I to generate spacetimes with symmetries in all dimensions. These results are used to find a geometric characterization of the Kerr-de Sitter metrics in all dimensions in terms of its geometric data at null infinity.

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