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Differential Geometry.


1d
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
Dec
20
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Dec
9
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Nov
14
revised Understanding the Jacobian
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Nov
14
comment Understanding the Jacobian
@VladimirVargas this is right and i will edit the answer now
Nov
12
answered Understanding the Jacobian
Oct
17
accepted A simple metric question
Oct
17
comment A simple metric question
@ploosu2 so it is correct, right?
Oct
17
revised A simple metric question
added 37 characters in body
Oct
17
asked A simple metric question
Oct
15
revised Calc I limit question involing trig functions
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