scholarly journals Tolman-Ehrenfest-Klein law in non-Riemannian geometries

2021 ◽  
Vol 104 (12) ◽  
Author(s):  
J. A. S. Lima ◽  
J. Santos
Keyword(s):  
Riemannian Geometries

scholarly journals COMBINATORIAL AND TOPOLOGICAL PHASE STRUCTURE OF NON-PERTURBATIVE n-DIMENSIONAL QUANTUM GRAVITY

1992 ◽  
Vol 06 (11n12) ◽  
pp. 2109-2121
Author(s):  
M. CARFORA ◽  
M. MARTELLINI ◽  
A. MARZUOLI
Keyword(s):  
Quantum Gravity ◽  
Phase Structure ◽  
Gravity Models ◽  
Topological Phase ◽  
Geometrical Characterization ◽  
Homotopy Types ◽  
Geometrical Constraints ◽  
Riemannian Geometries

We provide a non-perturbative geometrical characterization of the partition function of ndimensional quantum gravity based on a rough classification of Riemannian geometries. We show that, under natural geometrical constraints, the theory admits a continuum limit with a non-trivial phase structure parametrized by the homotopy types of the class of manifolds considered. The results obtained qualitatively coincide, when specialized to dimension two, with those of two-dimensional quantum gravity models based on random triangulations of surfaces.

Weyl–Euler–Lagrange equations on twistor space for tangent structure

2016 ◽  
Vol 13 (07) ◽  
pp. 1650095
Author(s):  
Zeki Kasap
Keyword(s):  
Mathematical Modeling ◽  
Dynamical System ◽  
Classical Mechanic ◽  
Twistor Space ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Equation System ◽  
Lagrange Equations ◽  
Four Manifolds ◽  
Riemannian Geometries

Twistor spaces are certain complex three-manifolds, which are associated with special conformal Riemannian geometries on four-manifolds. Also, classical mechanic is one of the major subfields for mechanics of dynamical system. A dynamical system has a state determined by a collection of real numbers, or more generally by a set of points in an appropriate state space for classical mechanic. Euler–Lagrange equations are an efficient use of classical mechanics to solve problems using mathematical modeling. On the other hand, Weyl submitted a metric with a conformal transformation for unified theory of classical mechanic. This paper aims to introduce Euler–Lagrage partial differential equations (mathematical modeling, the equations of motion according to the time) for the movement of objects on twistor space and also to offer a general solution of differential equation system using the Maple software. Additionally, the implicit solution of the equation will be obtained as a result of a special selection of graphics to be drawn.

scholarly journals EXTENDED SCHOUTEN CLASSIFICATION FOR NON-RIEMANNIAN GEOMETRIES

2008 ◽  
Vol 23 (01) ◽  
pp. 17-23 ◽  
Author(s):  
SABRINA CASANOVA ◽  
ORCHIDEA MARIA LECIAN ◽  
GIOVANNI MONTANI ◽  
REMO RUFFINI ◽  
ROUSTAM ZALALETDINOV
Keyword(s):  
Order Approximation ◽  
Structure Matrix ◽  
First Order ◽  
First Order Approximation ◽  
Riemannian Geometries ◽  
Inverse Structure

A generalized connection, including Christoffel coefficients, torsion, non-metricity tensor and metric-asymmetricity object, is analyzed according to the Schouten classification. The inverse structure matrix is found in the linearized regime, autoparallel trajectories are defined and the contribution of the components of the connection are clarified at first-order approximation.

Riemannian Geometries of Variable Curvature in Visual Space: Visual Alleys, Horopters, and Triangles in Big Open Fields

Perception ◽  
1976 ◽  
Vol 5 (1) ◽  
pp. 9-23 ◽  
Author(s):  
Antonio M Battro ◽  
Scipione di Pierro Netto ◽  
Reinier J A Rozestraten
Keyword(s):  
Riemannian Geometry ◽  
Dimensional Space ◽  
Visual Space ◽  
Open Spaces ◽  
Variable Curvature ◽  
Individual Function ◽  
Negative Constant ◽  
The Subject ◽  
The Individual ◽  
Riemannian Geometries

Luneburg's model for computation of the curvature K of visual two-dimensional space (horizontal visual surface) was tested with equidistant and parallel alleys in large open spaces. Forty-six subjects used stakes to produce 406 experimental alleys of variable sizes (from 5 × 1 to 240 m × 48 m). The results show that, contrary to results obtained under laboratory conditions with small alleys and light spots, the individual curvature of visual space does not have a negative constant value. K varies in the interval −1 to +1 in ninety computed settings: K ≥ 0 ( N = 38); K < 0 ( N = 52). Therefore the Lobachevskian geometry currently attributed to visual space ought to be replaced by a Riemannian geometry of variable curvature. Moreover K is an individual function dependant on the size of the alley (distance from the subject), and visual perception would be better understood as scale-dependent. Independently of Luneburg's model we have tested the constancy of the curvature hypothesis in experiments with horopters and visual triangles. The results obtained invalidate Luneburg's hypothesis also.

scholarly journals Moduli of quantum Riemannian geometries on ⩽4 points

2004 ◽  
Vol 45 (12) ◽  
pp. 4596-4627 ◽  
Author(s):  
S. Majid ◽  
E. Raineri
Keyword(s):  
Riemannian Geometries

scholarly journals On Riemannian Geometries of Visual Space

2021 ◽  
Author(s):  
Jacek Turski
Keyword(s):  
Riemannian Geometry ◽  
Physical Space ◽  
Visual Space ◽  
Gaze Direction ◽  
Relative Depth ◽  
Metric Tensor ◽  
The Gaze ◽  
Zero Curvature ◽  
Riemannian Geometries ◽  
Straight Lines

This is a study of the phenomenal geometries constructed in the Riemannian geometry framework from simulated iso-disparity conics in the horizontal visual plane of the binocular system with the asymmetric eyes (AEs). The iso-disparity conic's arcs in the Cyclopean direction are the frontal visual geodesics. For the eyes' resting vergence posture, which depends on parameters of the AE, the iso-disparity conics are frontal straight lines in physical space. For all other fixations, the iso-disparity conics consist of families of the ellipses or hyperbolas depending on both the AE's parameters and the bifoveal fixation. An assumption underlying the relevant architecture of the human visual system is combined with results from simulated iso-disparity straight lines, giving the relative depth as a function of the distance. This establishes the metric tensor in binocular space of fixations for the eyes' resting vergence posture. The resulting geodesics in the gaze direction, give the distance to the horizon and zero curvature. For all other fixations, only the sign of the curvature can be inferred from the global behavior of the simulated iso-disparity conics.

Comment on functional integration and the Onsager-Machlup Lagrangian in Riemannian geometries

1980 ◽  
Vol 21 (4) ◽  
pp. 1344-1346 ◽  
Author(s):  
F. Langouche ◽  
D. Roekaerts ◽  
E. Tirapegui
Keyword(s):  
Functional Integration ◽  
Riemannian Geometries
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