Riemann geometry and hydrostatic

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SUMMARY

The discussion centers on Elie Cartan's assertion in "La Géométrie des espaces de Riemann" that a constant Ricci scalar curvature (R = cte) allows for a comparison between space-time and the hydrostatic description of a liquid. Participants question the validity of this comparison and the reliability of alternative interpretations over Cartan's established work. The term "cte" refers to a constant value, which is crucial in understanding the context of the discussion.

PREREQUISITES
  • Understanding of Riemannian geometry
  • Familiarity with Ricci curvature concepts
  • Basic knowledge of hydrostatics
  • Awareness of Elie Cartan's contributions to differential geometry
NEXT STEPS
  • Research the implications of constant Ricci scalar curvature in general relativity
  • Explore the relationship between Riemannian geometry and fluid dynamics
  • Study Elie Cartan's works on differential geometry
  • Investigate the mathematical foundations of hydrostatic equilibrium
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Mathematicians, physicists, and students of theoretical physics interested in the intersection of geometry and fluid dynamics, particularly in the context of general relativity.

delplace
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I read in Elie CARTAN book : "la Géométrie des espace de Riemann" that when R = cte, you can compare space-time to hydrostatic description of a liquid. Is it true ?
 
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Why would you doubt Elie Cartan?

[EDIT]: More precisely why would you take the word of a random reply here over the word of Cartan if the two should differ?
 
Last edited:
What do you mean by "cte"?
 

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