scholarly journals Noether and Hilbert (metric) energy-momentum tensors are not, in general, equivalent

2021 ◽  
Vol 962 ◽  
pp. 115240
Author(s):  
Mark Robert Baker ◽  
Natalia Kiriushcheva ◽  
Sergei Kuzmin
Keyword(s):  
Hilbert Metric

scholarly journals A Simple Formula for the Hilbert Metric with Respect to a Sub-Gaussian Cone

Mathematics ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 35
Author(s):  
Stéphane Chrétien ◽  
Juan-Pablo Ortega
Keyword(s):  
Simple Formula ◽  
Hilbert Metric

scholarly journals On Non-positive Curvature Properties of the Hilbert Metric

2018 ◽  
Vol 29 (1) ◽  
pp. 569-576
Author(s):  
Layth M. Alabdulsada ◽  
László Kozma
Keyword(s):  
Positive Curvature ◽  
Hilbert Metric

REAL PROJECTIVE MANIFOLDS DEVELOPING INTO AN AFFINE SPACE

1993 ◽  
Vol 04 (02) ◽  
pp. 179-191 ◽  
Author(s):  
YOUNKI CHAE ◽  
SUHYOUNG CHOI ◽  
CHAN-YOUNG PARK
Keyword(s):  
Projective Space ◽  
Affine Space ◽  
Dimensional Subspace ◽  
Affine Group ◽  
Projective Manifold ◽  
Hilbert Metric ◽  
Projective Manifolds

Suppose that an n-dimensional closed real projective manifold M, n ≥ 2, develops into an affine space RPn − RPn − 1 for an (n − 1)-dimensional subspace RPn − 1 of the projective space RPn. Then either M is convex or affine or M admits a flat foliation [Formula: see text] with a transverse invariant Hilbert metric. Further, if the codimension of [Formula: see text] is n − 1, then M is convex. We prove this statement by a use of a variation of Carrière's discompacté, a measure of non-compactedness of an affine group acting on an affine space.

scholarly journals Conformal measure and decay of correlation for covering weighted systems

1998 ◽  
Vol 18 (6) ◽  
pp. 1399-1420 ◽  
Author(s):  
CARLANGELO LIVERANI ◽  
BENOIT SAUSSOL ◽  
SANDRO VAIENTI
Keyword(s):  
Invariant Measure ◽  
Equilibrium State ◽  
Large Class ◽  
Compact Set ◽  
Mixing Rate ◽  
Hilbert Metric ◽  
Frobenius Operator ◽  
Conformal Measure ◽  
Conformal Measures ◽  
Compactness Arguments

We show that for a large class of piecewise monotonic transformations on a totally ordered, compact set one can construct conformal measures and obtain the exponential mixing rate for the associated equilibrium state. The method is based on the study of the Perron–Frobenius operator. The conformal measure, the density of the invariant measure and the rate of mixing are deduced by using an appropriate Hilbert metric, without any compactness arguments, even in the case of a countable to one transformation.

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