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Apr
18
answered $\frac{d^2y}{dt^2}+4y=t\sin(2t)$'s particular solution
Mar
15
comment Is there a charaterization of riemannian product manifolds?
@RyanBudney Thank you.
Mar
15
comment Is there a charaterization of riemannian product manifolds?
Thank you for your interesting answer.
Mar
15
accepted Is there a charaterization of riemannian product manifolds?
Mar
11
asked Is there a charaterization of riemannian product manifolds?
Feb
10
comment Find the surface area obtained by rotating $y=1+3x^2$ from $x=0$ to $x=2$ about the y-axis.
Yes you are right
Feb
2
awarded  Benefactor
Feb
2
comment Hessian of a function on Riemannian manifolds
your answer is still the best incomplete one
Feb
2
accepted Hessian of a function on Riemannian manifolds
Jan
30
comment Hessian of a function on Riemannian manifolds
Your answer is still the best and I really hope to accept it. No. 2 answer is done. No. 2 is not. Could you prove or disprove it in the non-compact case?
Jan
28
comment Hessian of a function on Riemannian manifolds
Thank you Jack. I think this is good for compact case. I hope you get sufficient and necessary conditions in non-compact case. On the other hand, would you kindly give me a similar proof of 2 without considering $f$ as an eigenfunction of the laplacian?
Jan
25
awarded  Promoter
Jan
25
comment Hessian of a function on Riemannian manifolds
Thank you for patience and efficiency. The problem is still unsolved.
Jan
25
comment Hessian of a function on Riemannian manifolds
But your conclusion based on the assumption that $f$ is an eigenfunction of the Laplacian. So, you may rephrase your conclusion as "there is no such $h$ for a function f satisfying $\Delta f= \lambda f$", am I right?
Jan
25
revised Hessian of a function on Riemannian manifolds
added 89 characters in body
Jan
25
comment Hessian of a function on Riemannian manifolds
So, do you think that there is no such $h$ in item 1 even in compact case?
Jan
24
comment Hessian of a function on Riemannian manifolds
Thank you for your nice answer. I will try to play the game but kindly let me contact you in failure case.
Jan
23
comment Hessian of a function on Riemannian manifolds
@studiosus , Would you kindly clarify this comment as an answer specially part one(f is a non constant eigenfunction ...). If not, a good simple reference is enough. thanks in advance.
Jan
22
asked Hessian of a function on Riemannian manifolds
Dec
20
awarded  Yearling