May 19, 2018 · 1 After a lot of searching I came across Advanced general relativity lecture notes by Sergei Winitzki and an intro to differential geometry and curvature by Hestenes ,link below,. Misner's …

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. …

Sep 20, 2019 · What is a standard definition for a twisted product of Pseudo-Riemannian manifolds? EDIT: So as some comments say, the definition of a twisted product seems to be canonical. I need a …

Mar 3, 2015 · Call such a p p -centered coordinate system 0 0 -adapted to g g at p p. Now, ask what would be the effect of expressing g g in the coordinates y = (yi) y = (y i) that are related to the …

Why does the naive choice of homogeneous coordinate ring of a product of projective schemes not work? Ask Question Asked 12 years, 9 months ago Modified 12 years, 9 months ago

May 30, 2023 · Let (Mn, g) (M n, g) be a Riemannian manifold with a fixed point p p. Can we find a local coordinate system (x1,x2, ⋯,xn) (x 1, x 2,, x n) around p p satisfying the following two at the same …

Nov 27, 2022 · Bounds for metric in normal coordinate Ask Question Asked 3 years, 2 months ago Modified 1 year, 9 months ago

Basically, the geodesic distance is the usual Euclidean distance, at least on such normal coordinate system. That's what I thought. Thank you.

Let (M, g) (M, g) be a Riemannian manifold, p p a point on the manifold and v ∈ TpM v ∈ T p M. Let γ γ be the geodesic starting at p p in the direction v v. There exists a time tf t f such that there exists a …

Aug 4, 2019 · This question seems to be more in the trivial side, but what is the explicit coordinate transformation from $\mathrm {d}s^2_P$ to either $\mathrm {d}s^2_ {G1}$ or $\mathrm {d}s^2_ {G2}$?