Beltrami's theorem

Beltrami's theorem

In mathematics — specifically, in Riemannian geometry — Beltrami's theorem is a result named after the Italian mathematician Eugenio Beltrami which states that geodesic maps preserve the property of having constant curvature. More precisely, if ("M", "g") and ("N", "h") are two Riemannian manifolds and "φ" : "M" → "N" is a geodesic map between them, and if either of the manifolds ("M", "g") or ("N", "h") has constant curvature, then so does the other one.

References

* cite book
last = Ambartzumian
first = R. V.
title = Combinatorial integral geometry
series = Wiley Series in Probability and Mathematical Statistics: Tracts on Probability and Statistics
publisher = John Wiley & Sons Inc.
location = New York
year = 1982
pages = p. 26
isbn = 0-471-27977-3
MathSciNet|id=679133
* cite book
last = Kreyszig
first = Erwin
title = Differential geometry
publisher = Dover Publications Inc.
location = New York
year = 1991
pages = pp. xiv+352
isbn = 0-486-66721-9
MathSciNet|id=1118149 (See section 91)

External links

*


Wikimedia Foundation. 2010.

Игры ⚽ Поможем сделать НИР

Look at other dictionaries:

  • Eugenio Beltrami — Infobox Scientist name = Eugenio Beltrami image width = 170px caption = Eugenio Beltrami birth date = birth date|1835|11|16|df=y birth place = Cremona, Lombardy, Austrian Empire death date = death date and age|1899|6|4|1835|11|16|df=y death place …   Wikipedia

  • Laplace-Beltrami operator — In differential geometry, the Laplace operator can be generalized to operate on functions defined on surfaces, or more generally on Riemannian and pseudo Riemannian manifolds. This more general operator goes by the name Laplace Beltrami operator …   Wikipedia

  • Cheng's eigenvalue comparison theorem — In Riemannian geometry, Cheng s eigenvalue comparison theorem states in general terms that when a domain is large, the first Dirichlet eigenvalue of its Laplace–Beltrami operator is small. This general characterization is not precise, in part… …   Wikipedia

  • Measurable Riemann mapping theorem — In the mathematical theory of quasiconformal mappings in two dimensions, the measurable Riemann mapping theorem, proved by Morrey (1936, 1938), generalizes the Riemann mapping theorem from conformal to quasiconformal homeomorphisms, and is… …   Wikipedia

  • List of mathematics articles (B) — NOTOC B B spline B* algebra B* search algorithm B,C,K,W system BA model Ba space Babuška Lax Milgram theorem Baby Monster group Baby step giant step Babylonian mathematics Babylonian numerals Bach tensor Bach s algorithm Bachmann–Howard ordinal… …   Wikipedia

  • Pseudosphere — In geometry, a pseudosphere of radius R is a surface of curvature −1/ R 2 (precisely, a complete, simply connected surface of that curvature), by analogy with the sphere of radius R , which is a surface of curvature 1/ R 2. The term was… …   Wikipedia

  • Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… …   Wikipedia

  • Laplace operator — This article is about the mathematical operator. For the Laplace probability distribution, see Laplace distribution. For graph theoretical notion, see Laplacian matrix. Del Squared redirects here. For other uses, see Del Squared (disambiguation) …   Wikipedia

  • Logic and the philosophy of mathematics in the nineteenth century — John Stillwell INTRODUCTION In its history of over two thousand years, mathematics has seldom been disturbed by philosophical disputes. Ever since Plato, who is said to have put the slogan ‘Let no one who is not a geometer enter here’ over the… …   History of philosophy

  • Proof of impossibility — A proof of impossibility, sometimes called a negative proof or negative result , is a proof demonstrating that a particular problem cannot be solved, or cannot be solved in general. Often proofs of impossibility have put to rest decades or… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”