scholarly journals A Study On Geometry of Spatial Kinematics in Lorentzian Space

2017 ◽  
Vol 21 (3) ◽  
pp. 808
Author(s):  
Tunahan TURHAN ◽  
Nihat AYYILDIZ
Keyword(s):  
Lorentzian Space ◽  
Spatial Kinematics

A new approach to the bienergy and biangle of a moving particle lying in a surface of lorentzian space

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Talat Körpınar ◽  
Yasin Ünlütürk
Keyword(s):  
Vector Fields ◽  
Elastic Surface ◽  
Geometrical Characterization ◽  
Lorentzian Space ◽  
New Approach ◽  
Darboux Vector ◽  
Moving Particle ◽  
The Relationship ◽  
Surface Curve

AbstractIn this research, we study bienergy and biangles of moving particles lying on the surface of Lorentzian 3-space by using their energy and angle values. We present the geometrical characterization of bienergy of the particle in Darboux vector fields depending on surface. We also give the relationship between bienergy of the surface curve and bienergy of the elastic surface curve. We conclude the paper by providing bienergy-curve graphics for different cases.

The Curvature Theory of Line Trajectories in Spatial Kinematics

1981 ◽  
Vol 103 (4) ◽  
pp. 718-724 ◽  
Author(s):  
J. M. McCarthy ◽  
B. Roth
Keyword(s):  
Planar Motion ◽  
Spatial Motion ◽  
Third Order ◽  
Local Shape ◽  
The Third ◽  
Moving Body ◽  
Physical Representation ◽  
Curvature Theory ◽  
Spatial Kinematics ◽  
Differential Properties

This paper develops the differential properties of ruled surfaces in a form which is applicable to spatial kinematics. Derivations are presented for the three curvature parameters which define the local shape of a ruled surface. Related parameters are also developed which allow a physical representation of this shape as generated by a cylindric-cylindric crank. These curvature parameters are then used to define all the lines in the moving body which instantaneously generate speciality shaped trajectories. Such lines may be used in the synthesis of spatial motions in the same way that the points on the inflection circle and cubic of stationary curvature are used to synthesize planar motion. As an example of this application several special sets of lines are defined: the locus of all lines which for a general spatial motion instantaneously generate helicoids to the second order and the locus of lines generating right hyperboloids to the third order.

scholarly journals Pseudoinversion of degenerate metrics

2003 ◽  
Vol 2003 (55) ◽  
pp. 3479-3501 ◽  
Author(s):  
C. Atindogbe ◽  
J.-P. Ezin ◽  
Joël Tossa
Keyword(s):  
Differential Geometry ◽  
Large Class ◽  
Smooth Manifold ◽  
Differential Operators ◽  
Type Operator ◽  
Lorentzian Space ◽  
Lightlike Hypersurface ◽  
Definition Of ◽  
Lightlike Hypersurfaces ◽  
Theoretical Results

Let(M,g)be a smooth manifoldMendowed with a metricg. A large class of differential operators in differential geometry is intrinsically defined by means of the dual metricg∗on the dual bundleTM∗of 1-forms onM. If the metricgis (semi)-Riemannian, the metricg∗is just the inverse ofg. This paper studies the definition of the above-mentioned geometric differential operators in the case of manifolds endowed with degenerate metrics for whichg∗is not defined. We apply the theoretical results to Laplacian-type operator on a lightlike hypersurface to deduce a Takahashi-like theorem (Takahashi (1966)) for lightlike hypersurfaces in Lorentzian spaceℝ1n+2.

scholarly journals HYPERSURFACES IN NON-FLAT LORENTZIAN SPACE FORMS SATISFYING Lkψ = Aψ + b

2012 ◽  
Vol 16 (3) ◽  
pp. 1173-1203 ◽  
Author(s):  
Pascual Lucas ◽  
H. Fabian Ramirez-Ospina
Keyword(s):  
Space Forms ◽  
Lorentzian Space ◽  
Lorentzian Space Forms

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.

On the quadric CMC spacelike hypersurfaces in Lorentzian space forms

2016 ◽  
pp. 1-10
Author(s):  
Cícero P. Aquino ◽  
Henrique F. de Lima ◽  
Fábio R. dos Santos
Keyword(s):  
Space Forms ◽  
Lorentzian Space ◽  
Spacelike Hypersurfaces ◽  
Lorentzian Space Forms

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

DOES THE HETEROTIC SUPERSTRING THEORY CONTAIN CLOSED TIME-LIKE LINES?

2009 ◽  
Vol 18 (04) ◽  
pp. 559-586 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Scalar Field ◽  
Line Element ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Causality Condition ◽  
Superstring Theory ◽  
Lorentzian Space ◽  
Higher Derivative ◽  
Gravitational Theories ◽  
Rotational Space

Causal solutions of the Gödel type, for which the line element is ds2 = dt2 - 2b e mxdtdv - c e 2mxdv2 - dx2 - dz2 with c = 0, are known to exist for gravitational theories containing a cosmological constant Λ and quadratic higher-derivative terms defined by the Lagrangian L = -(1/2)κ-2(R + 2Λ) + A1R2 + A2RijRij. Here, we show that acausal solutions, for which c < 0, containing closed time-like lines, can be constructed only if A2 = 0. Extension of this analysis to the heterotic superstring theory, including a generic massless scalar field ϕ plus quadratic and quartic gravitational terms [Formula: see text] and [Formula: see text], again yields a causal solution with c = 0, and also Λ = 0, as required for anomaly freedom, while solutions with c < 0 are ruled out. More general rotational space–times appear to be intractable analytically, and therefore it remains a matter of conjecture that the heterotic superstring admits only classical Lorentzian solutions which respect causality. For the energy density ρ(ϕ) of the scalar field is positive semi-definite only when g00 ≥ 0, which is equivalent to the causality condition g11 ≤ 0 or c ≥ 0 in a Lorentzian space–time for which det gij < 0; while ρ(ϕ) is unbounded from below in the presence of closed time-like lines, when g11 > 0, implying instability of ϕ, which will react back on the metric until it becomes causal.

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