1) That conforms, especially to the shape of something.
Fr.: compactification conforme
A mapping of an infinite → space-time onto a finite one that may make the far away parts of the former accessible to study. The technique invented by Penrose defines an equivalence class of → metrics, gab being equivalent to ĝab = Ω2gab, where Ω is a positive scalar function of the space-time that modifies the distance scale making the asymptotics of the physical metric accessible to study.
→ conformal; → compactification.
conformal cyclic cosmology (CCC)
keyhânšenâsi-ye carxe-yi-ye hamdis
Fr.: cosmologie cyclique conforme
A cosmological model developped by Roger Penrose and colleagues according which the Universe undergoes repeated cycles of expansion. Each cycle, referred to an aeon, starts from its own "→ big bang" and finally comes to a stage of accelerated expansion which continues indefinitely. There is no stage of contraction (to a "→ big crunch") in this model. Instead, each aeon of the universe, in a sense "forgets" how big it is, both at its big bang and in its very remote future where it becomes physically identical with the big bang of the next aeon, despite there being an infinite scale change involved, on passing from one aeon to the next. This model considers a conformal structure rather than a metric structure. Conformal structure may be viewed as family of metrics that are equivalent to one another via a scale change, which may vary from place to place. Thus, in conformal space-time geometry, there is not a particular metric gab, but an equivalence class of metrics where the metrics ğab and gab are considered to be equivalent if there is a smooth positive scalar field Ω for which ğab = Ω gab (R. Penrose, 2012, The Basic Ideas of Conformal Cyclic Cosmology).
Fr.: géométrie conforme
The study of the set of angle-preserving transformations on a space.
Fr.: application conforme
A continuous mapping u = f(x) of a domain D in an n-dimensional Euclidean space (n≥ 2) into the n-dimensional Euclidean space is called conformal at a point x0∈ D if it has the properties of constancy of dilation and preservation of angles at this point.