Riemannian Geometry

@article{HolopainenRiemannianG,
  title={Riemannian Geometry},
  author={I. Holopainen},
  journal={Nature},
  volume={119},
  pages={117-117}
}
THE recent physical interpretation of intrinsic differential geometry of spaces has stimulated the study of this subject. Riemann proposed the generalisation, to spaces of any order, of Gauss's theory of surfaces, and introduced certain fundamental ideas in this general theory. Bianchi, Beltrami, and others made substantial contributions to the subject, which was extended by Ricci with the use of tensor analysis and his absolute calculus. Recently there has been an extensive study and… CONTINUE READING
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References

SHOWING 1-10 OF 33 REFERENCES
Partial Differential Equations
  • 17,680
  • PDF
Sur les surfaces a courbure negative. (On surfaces of negative curvature )
  • C. R. Acad. Sci. Paris
  • 1926
Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen. (German). (The asymptotic distribution law of the eigenvalues of linear partial differential equations)
  • Math. Ann
  • 1912
2 Induced metric on surfaces
  • 2 Induced metric on surfaces
A proof of the well conjecture using Ricci flow
  • A proof of the well conjecture using Ricci flow
A semi-discrete, linear curve shortening flow
  • American Math. Monthly
Aleksandrov spaces with curvatures bounded from below
  • Aleksandrov spaces with curvatures bounded from below
Asymptotic stability of Ricci pseudosolitons
  • Asymptotic stability of Ricci pseudosolitons
Classes of domains and imbedding theorems for function spaces
  • Classes of domains and imbedding theorems for function spaces
Compact Ricci solitons
  • Compact Ricci solitons