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martinbn

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So, you want to do something, but you don't know what, and you are asking for ideas!!!

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Ok, i am sorry if what i read is offensive, i wanted a discussion to understand and if something like that already exists. Perhaps i should not write it, because it might sound like i want to steal ideas.So, you want to do something, but you don't know what, and you are asking for ideas!!!

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Perhaps the thread should be deleted?

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martinbn

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No, I don't think you are trying to steal ideas. But it is not clear what you are asking for, so how can anyone help you?Ok, i am sorry if what i read is offensive, i wanted a discussion to understand and if something like that already exists. Perhaps i should not write it, because it might sound like i want to steal ideas.

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What i am trying to do is generalise the Gaussian curvature for the right kind of geometric sets.

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I think someone needs a second or perhaps a third also example to make the generalisation.

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martinbn

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I suppose forums could in principle be used for that.Are forums the right place or not for collaboration in producing original works in sciences? I should be more careful from now on when writing in forums i think.

What are the right kind of geometrical sets? This is not how original work is done by the way. You don't just try to randomly generalize something. You probably don't have experience in doing research. It would be best to go through the usual process. Get the education, work with an advisor, and then you can do research.What i am trying to do is generalise the Gaussian curvature for the right kind of geometric sets.

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Yes, indeed i do not have experience in doing research. I study at a university at a maths department.I want to get the degree but also i am interested in doing scientific research although i do not have a doctorate degree.I suppose forums could in principle be used for that.

What are the right kind of geometrical sets? This is not how original work is done by the way. You don't just try to randomly generalize something. You probably don't have experience in doing research. It would be best to go through the usual process. Get the education, work with an advisor, and then you can do research.

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fresh_42

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I think they have different definitions in the case of differential geometry and in that of algebraic geometry and yes in those cases so far the generalisation was that of manifolds and algebraic varieties.

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Different definitions of curves or surfaces could produce different generalisations?

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fresh_42

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Please define your surface.

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In differential geometry a surface is a two dimensional differentiable manifold with a metric tensor i think.In algebraic geometry it is a polynomial equation of three variables i think. I do not yet know how to define the surface in different ways.Please define your surface.

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fresh_42

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Perhaps the thread should be closed, i do not know the answer yet.

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fresh_42

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I think that you try to reinvent the wheel. When I was a kid I tried to figure out whether there could be a binary operation ##\circ## such that ##\log(a+b)=\log(a)\circ \log (b)##. I was fascinated by the fact that we can turn powers into multiplications ##\log(a^b)=b\log(a)## and multiplications into additions ##\log(a\cdot b)=\log(a)+\log(b)##. So why not turn additions into something evenPerhaps the thread should be closed, i do not know the answer yet.

Now, many years later, I know that there cannot be such an operation. Why? Because of the Leibniz rule of differentiation, or even more general: because of the definition of derivations. Differentiation of products yield sums, but differentiation of linear functions are themselves linear functions. There is no

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