Place of Analytic geometry in modern undergraduate curriculum
Nearly all of them had that title. The point was that analytic geometry = coordinate geometry and these books had preliminary sections on coordinate geometry before they jumped into discussing calculus. …
dg.differential geometry - History of the definition of charts and ...
Oct 9, 2025 · The use of the modern term chart for the coordinate maps seems to have originated around 1956 in work of Serre and Hirzebruch in algebraic topology. What is the precise history?
riemannian geometry - Existence of normal and harmonic coordinates ...
May 30, 2023 · Explore related questions riemannian-geometry See similar questions with these tags.
Why are they called isothermal coordinates? - MathOverflow
A Riemannian manifold has an intrinsic Laplacian, called the Laplace-Beltrami operator. Isothermal coordinates are harmonic in the sense that they belong to the kernel of this operator. On an oriented …
ag.algebraic geometry - Is the coordinate ring of a variety a finitely ...
Oct 21, 2016 · Is the coordinate ring of a variety a finitely generated algebra? Ask Question Asked 9 years, 4 months ago Modified 9 years, 4 months ago
Riemann's formula for the metric in a normal neighborhood
Mar 3, 2015 · Martin, I find Christoffel symbols highly unenlightening, so that's not a simple definition to me. It seems to me that both normal co-ordinates (up to second order only) and the Riemann …
dg.differential geometry - Existence of Fermi coordinates on a ...
1) I'm content with the thickness of the neighborhood shrinking. That's great to hear. 2) I'm working in a probabilistic context where the background coordinate system plays a crucial role.
dg.differential geometry - Almost Complex Structure extending to ...
Dec 6, 2024 · This is called an integrability condition. An almost complex structure is a complex structure if there exist local complex coordinate functions where the almost complex structure can be written in …
Exterior derivative independence from coordinate systems
Jul 8, 2019 · In the book Mathematical Methods of Classical Mechanics by V.I. Arnold, the author introduces (p.189) the concept of exterior derivative as "the principal linear part of the increment" of …
mg.metric geometry - Mapping a cube to a sphere - MathOverflow
May 12, 2023 · I only require equidistant points on the cube's coordinate lines to be mapped to equidistant points on the sphere's coordinate lines (as per the original query and pictures).