747 reputation
211
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location India
age
visits member for 2 years
seen Apr 10 at 2:11

Grad Student with an interest in Riemannian Geometry


Mar
28
awarded  Yearling
Mar
12
accepted Finding a space curve given some conditions on curvature and torsion
Mar
12
asked Finding a space curve given some conditions on curvature and torsion
Feb
27
revised How to show a curve has a bertrand mate? (differential geometry)
Improved Formatting
Feb
27
suggested suggested edit on How to show a curve has a bertrand mate? (differential geometry)
Feb
9
accepted Definition of the Energy of a curve
Feb
9
comment Definition of the Energy of a curve
Thanks for the reply. But where exactly does the distinction prop up between the energy and length notions then, as minimising one is same as minimising the other??And more importantly the dependence of the energy on parametrisation gives it a different flavour than length. Is there some way to realise this geometrically, some physical example?
Feb
9
asked Definition of the Energy of a curve
Feb
5
comment Directional derivatives, linear maps, and uniform convergence
Well let $v=(v_1,v_2)$.Then if $|tv_2|>t^2v_1{^2}$, $f(tv) = tv_1$ and the limit is $v_1$ else it is 0. So the limit exists, right??
Feb
5
comment Directional derivatives, linear maps, and uniform convergence
Actually it vanishes at many more points than that. Try drawing a picture. It should become visually clear as to why the convergence cannot be uniform.
Feb
5
comment Directional derivatives, linear maps, and uniform convergence
Seemingly the function vanishes on the parabolas $y=x^2$ and $y = -x^2$. Any small neighbourhood around the origin would have to contain a part of these parabolas. Does that help?
Jan
26
comment Ruled surface defined by a Exponential map
Sure , thanks. I apologise for nitpicking.
Jan
26
comment Ruled surface defined by a Exponential map
But in general when one talks of a Normal to a surface it should be in $T_p(M)^{\perp}$ right? Would that normal be $B(\alpha(s))$ here?
Jan
26
comment Ruled surface defined by a Exponential map
I think it would be more prudent to look at $M$ in $E^4$ as they are later supposed to have constant sectional curvatures. Though the above question does not assume that.But what you assumed does make sense to me actually.
Jan
26
accepted Ruled surface defined by a Exponential map
Jan
26
comment Ruled surface defined by a Exponential map
But then $N(\alpha(s))$ may be(not always) in $T_p(M)^{\perp}$, or am I wrong about that?
Jan
26
comment Ruled surface defined by a Exponential map
Yes I realise that. But that $v$ should be in $T_p(M)$ right?
Jan
26
comment A problem on denseness
This is not an answer as such. But in general for fixed real $r$, sets of the form ${a+ br : a,b \in \mathbb Z , r \in \mathbb R} $ is dense in $\mathbb R$. See Dirichlet's approximation theory in number theory. Hope this helps.
Jan
26
comment What is an isomorphism?
Yes the category matters. It just so happens that we read about specific categories and morphisms without every having heard about General Category theory,as in my case. But I think thats not a bad thing anyways.
Jan
26
comment Ruled surface defined by a Exponential map
I had almost given up hope. Thanks a lot, but could you elaborate a bit more as to how it is an immersion in $\mathbb R^4$?? Also,I was asking whether that sum makes sense as $\alpha(s)$ is a point on M for each s whereas $N(\alpha(s)) $ may be in the codimension space of M and is a vector??I am missing something simple maybe, but still cant see it.