Riemman Definition and 14 Threads

Hello I have been going through the cosmology chapter in Choquet Bruhats GR and Einstein equations and in definition 3.1 of chapter 5 she defines the sectional curvature with a Riemann( X, Y;X, Y) (X and Y two vectors) I don't understand this notation, regarding the use of the semi colon, is it...

I have been trying to use numerical methods with this function but now I realize that I if I could suggest a Polynomial in theory, I could get some value for the Integral at least in any interval. In general, does the Integral of the Riemman dseta function has a meaning by itself?

Homework Statement Your task is to estimate how far an object traveled during the time interval 0≤t≤8, but you only have the following data about the velocity of the object. *First image You decide to use a left endpoint Riemann sum to estimate the total displacement. So, you pick up a blue...

Given the metric of the gravitational field of a central gravitational body: ds2 = -ev(r)dt2 + eμ(r)dr2 + r2 (dθ2 + sin2θdΦ2) And the Chritofell connection components: Find the Riemannian curvature tensor component R0110 (which is non-zero). I believe the answer uses the Ricci tensor...

Please bear with me because I'm only in Pre-calculus and am taking basic high school physics. This is completely outside of my realm but curiosity has taken the better of me. I just learned last week about the difference between Euclidean Geometry and Riemmanian Geometry (from another thread...

I understand that Riemann was very shy, so he didn't talk much. Something that he said was: 'If only I had the theorems! Then I should find the proofs easily enough' . What do you think meant by that? I suspect he was comparing deductive reasoning (proofs) with imagination and the 'seeing over...

Hello all, I have been given a problem where I am asked to calculate "all" the components of the Riemann tensor in a gross non-diagonalized metric. I know there exists at most 20 independent components of Riemann, but I want to actually compose a list of these combinations. It is easy...

there is correct the expresion \int^{-\pi+\epsilon}_{\pi-\epsilon} d\theta...where \theta is a angular coordinate between (-\pi,\pi)...¿what means this?... i believe that this mean that the angular coordinate theta runs from \pi-\epsilon to -\pi+\epsilon in the sense anti clock (figure)

A random question - Does the Riemman tensor and the covariant derivate commute? a yes/no answer would suffice, but any explanation would be welcome:) From the equations, it looks as though they do for flat metrics - but if we have other manifolds, it seems to me that the Christoffel...

If the integral is \int^{\pi-\epsilon}_{-\pi+\epsilon}d\theta. where \theta is a angular coordinate. In the riemman integral , i don't understand if tetha follows the path grenn in figure 1, or \theta follows the path red in figure 2.

Let α>0, J:=[-a,a] and f:J→ℝ a bounded function. Let α an increases monotonically on J and P* the set of all partitions P of J containing 0 and such that are symmetric,i.e, x in P iff -x in P. Prove that ∫fdα= sup L(P,f,α) with P in P*

Homework Statement Question regarding #16 Homework Equations Riemman Sum The Attempt at a Solution I know that the limit of the Riemman Sum is basically the integral. However, I do not know where to go from there. Do I need to use the Summation formulas? Thanks

The following sum Sqrt(5+5/n) * (5/n) + Sqrt(5 +10/n) * (5/n)... is a right Riemann sum for the definite integral a=3 and b= 8 what does f(x) equal? I got a and b but could not find f(x) It is also a Riemann sum for the definite integral Sqrt(5+5/n) * (5/n) (same as above)...

The velocity function is v(t)=t^2 -5t + 6 for a particle moving along a line. Find the displacement traveled by the particle during the time interval [0,5]. What is the displacement? What is the distance traveled? I think that the information should look like this: (1)(1^2 -5(1)...