Topic
Fubini–Study metric
About: Fubini–Study metric is a research topic. Over the lifetime, 942 publications have been published within this topic receiving 24354 citations.
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1 / 2
Papers
Book•
1 Jan 1999
TL;DR: In this paper, Loewner proposed a metric structure with a bounded Ricci Curvature for length structures on families of metric spaces, where the degree and dilatation of the length structure is a function of degree and degree.
Abstract: Length Structures: Path Metric Spaces.- Degree and Dilatation.- Metric Structures on Families of Metric Spaces.- Convergence and Concentration of Metrics and Measures.- Loewner Rediscovered.- Manifolds with Bounded Ricci Curvature.- Isoperimetric Inequalities and Amenability.- Morse Theory and Minimal Models.- Pinching and Collapse.
2,891 citations
TL;DR: The theory of quasiconformal maps in metric spaces that satisfy certain bounds on their mass and geometry has been studied in this article, and the main message is that such a theory is both relevant and viable.
Abstract: This paper develops the foundations of the theory of quasiconformal maps in metric spaces that satisfy certain bounds on their mass and geometry. The principal message is that such a theory is both relevant and viable. The first main issue is the problem of definition, which we next describe. Quasiconformal maps are commonly understood as homeomorphisms that distort the shape of infinitesimal balls by a uniformly bounded amount. This requirement makes sense in every metric space. Given a homeomorphism f from a metric space X to a metric space Y , then for x∈X and r>0 set
1,116 citations
TL;DR: In this paper, it was shown that the Schwarzschild metric has certain characteristics that correspond to a ring of mass that is rotating about its axis of symmetry, which is the case of the Riemann tensor.
Abstract: It is shown that by means of a complex coordinate transformation performed on the monopole or Schwarzschild metric one obtains a new metric (first discovered by Kerr). It has been suggested that this metric be interpreted as that arising from a spinning particle. We wish to suggest a more complicated interpretation, namely that the metric has certain characteristics that correspond to a ring of mass that is rotating about its axis of symmetry. The argument for this interpretation comes from three separate places: (1) the metric appears to have the appropriate multipole structure when analyzed in the manner discussed in the previous paper, (2) in a covariantly defined flat space associated with the metric, the Riemann tensor has a circular singularity, (3) there exists a closely analogous solution of Maxwell's equations that has characteristics of a field due to a rotating ring of charge.
970 citations
TL;DR: In this article, the authors establish a general criterion for a set of non-Hermitian operators to constitute a consistent quantum mechanical system, which allows for the normal quantum-mechanical interpretation.
862 citations
TL;DR: In this paper, the principal empirical laws of equilibrium thermodynamics can be brought into correspondence with the mathematical axioms of an abstract metric space, which permits one to associate with the thermodynamic formalism a geometrical aspect, with intrinsic metric structure, which is distinct from that arising from graphical representations of equilibrium surfaces in phase space.
Abstract: It is shown that the principal empirical laws of equilibrium thermodynamics can be brought into correspondence with the mathematical axioms of an abstract metric space. This formal correspondence permits one to associate with the thermodynamic formalism a geometrical aspect, with intrinsic metric structure, which is distinct from that arising from graphical representations of equilibrium surfaces in phase space.
834 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
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| 2025 | 1 |
| 2023 | 6 |
| 2022 | 10 |
| 2021 | 1 |
| 2020 | 3 |
| 2019 | 4 |