Definition & Meaning | English word CONFORMALLY

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Definitions of CONFORMALLY

1. In a conformal manner
2. With regard to a conformality

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Examples of Using CONFORMALLY in a Sentence

• As a corollary of the theorem, any two simply connected open subsets of the Riemann sphere which both lack at least two points of the sphere can be conformally mapped into each other.
• So considered as a Riemann surface, the open unit disk is isomorphic ("biholomorphic", or "conformally equivalent") to the upper half-plane, and the two are often used interchangeably.
• A conformal metric is conformally flat if there is a metric representing it that is flat, in the usual sense that the Riemann curvature tensor vanishes.
• In a conformally invariant two-dimensional quantum theory, the Witt algebra of infinitesimal conformal transformations has to be centrally extended.
• This set of conformally equivalent Riemannian surfaces is precisely the same as all compact Riemannian surfaces of genus 3 whose conformal automorphism group is isomorphic to the unique simple group of order 168.
• Any 2-dimensional (smooth) Riemannian manifold is conformally flat, a consequence of the existence of isothermal coordinates.
• But for the finite-range gravity model and Ogievetsky and Polubarinov model, it turns out that they need Noether's variational principle together with redefining and conformally improving the energy momentum tensor as a source field.
• The development of a conformally flat manifold is a conformal local diffeomorphism from the universal cover of the manifold to the n-sphere.
• Thus the notion of a Weyl connection is conformally invariant, and the change in one-form is mediated by a de Rham cocycle.
• Thus a closed Riemannian 2-manifold of non-positive curvature can never be embedded isometrically in ; however, as Adriano Garsia showed using the Beltrami equation for quasiconformal mappings, this is always possible for some conformally equivalent metric.
• The solar cells consist of a semitransparent thin film of nanotubes conformally coated on a n-type crystalline silicon substrate to create high-density p-n heterojunctions between nanotubes and n-Si to favor charge separation and extract electrons (through n-Si) and holes (through nanotubes).

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