# Tagged Questions

In differential geometry, the term curvature tensor may refer to the Riemann curvature tensor of a Riemannian manifold, the curvature of an affine connection or covariant derivative (on tensors), or the curvature form of an Ehresmann connection. (Def: http://en.m.wikipedia.org/wiki/Curvature_tensor)

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### sectional curvature of hyperbolic space

For a pair of $(X,Y)$ of linearly independent vectors in $T_pM$, $p\in M$, the sectional curvature is defined as $$K_p(X,Y)= - \frac{<R(X,Y)X,Y>}{|X|^2 |Y|^2 - <X,Y>^2}$$ The problem I'm ...
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### At what point does the curve y=(1/x) have max curvature? What happens to the curvature as x approaches infinity?

I have found kappa and kappa prime however have no clue where to go from here. Thanks Kprime = 6/-x^4(1+(1/x^4)^3/2-12/x^3(1+(1/x^4)^1/2) all over (1+(1/x^4))^3/2
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### sectional curvature, ricci tensor and scalar curvature of the hyperbolic space [closed]

Who can help me to compute the sectional curvature, Ricci tensor and the scalar curvature of the hyperbolic space $H^3$ ? Thanks!!
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### A Riemannian manifold with constant sectional curvature is Einstein. [closed]

A Riemannian manifold with constant sectional curvature is Einstein. Why? It's true the inverse?
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### surface gradient of the unit normal vector

I am reading a book that defines a curvature tensor as $\boldsymbol{K} = -\nabla_\pi \boldsymbol{\hat{n}}$ where $\boldsymbol{\hat{n}}$ is the unit normal vector of a surface and \begin{align*} \...
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### Raising to power as producing curvature

Is there some notion or theory that deals with the connection between the exponents of a polynomial and its curvature, i.e. how much it deviates from a straight line?
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### Prove a curvature identity

Show that N = (dT/dt)/(abs (dT/dt)) using dT/ds = k N
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### Thoughts on Theorema Egregium

Due to this theory any mapping from the globe to a paper neccesairly have disortions. My question is there a theory which states the number of necessary map that gets this error down to a certain ...
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