A brief summary of results on homotheties in General Relativity is given, including general information about space-times admitting an r-parameter group of homothetic transformations for r > 2, as well as some specific results on perfect fluids. Attention is then focussed on inhomogeneous models, in particular on those with a homothetic group H 4 (acting multiply transitively) and H 3. A classi...

In this paper, we study the binary relations R on a nonempty N-set A which are hindependent and h-positive (cf. the introduction below). They are called homothetic positive orders. Denote by B the set of intervals of R having the form [r,+∞[ with 0 < r ≤ +∞ or ]q,∞[ with q ∈ Q≥0. It is a Q>0-set endowed with a binary relation > extending the usual one on R>0 (identified with a subset of B via t...

In this paper, we revisit the classical mechanism to produce [Formula: see text]-dimensional spacetimes via Kaluza–Klein compactification. We made assumption that bulk geometry text] admits a Homothetic Vector Field (HVF) relaxing existence of zero i.e. holds on and homothetic bivector text]. Under these circumstances, identify origin positive cosmological constant in spacetime as factor repres...

In an incomplete market, with incompleteness stemming from stochastic factors imperfectly correlated with the underlying stocks, we derive representations of homothetic (power, exponential and logarithmic) forward performance processes in factor-form using ergodic BSDE. We also develop a connection between the forward processes and infinite horizon BSDE, and, moreover, with risk-sensitive optim...

We give a characterization of the non-empty binary relations  on a N∗-set A such that there exist two morphisms of N∗-sets u1, u2 : A → R+ verifying u1 ≤ u2 and x  y ⇔ u1(x) > u2(y). They are called homothetic interval orders. If  is a homothetic interval order, we also give a representation of  in terms of one morphism of N∗-sets u : A → R+ and a map σ : u(R+) × A → R+ such that x  y ⇔ σ(...