Any two dimensional orientable manifold is complex [duplicate]












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This question already has an answer here:




  • existence of complex structure in dimension 2

    1 answer



  • Why does every noncompact orientable surface have a complex structure?

    1 answer




Let $M$ be a $2$-dimensional orientable manifold. Is $M$ a Riemann surface? If it is true, how can I show it? Thank you very much.










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marked as duplicate by Dietrich Burde, Eric Wofsey, Lord Shark the Unknown, amWhy, Robert Soupe Dec 3 '18 at 3:03


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.















  • It is a $1$-dimensional complex manifold (in complex sense).
    – joseabp91
    Dec 2 '18 at 19:27








  • 1




    See: math.stackexchange.com/a/907476/534616
    – K B Dave
    Dec 2 '18 at 19:27










  • Not quite a duplicate of that one because the surface isn't required to be compact
    – K B Dave
    Dec 2 '18 at 19:29










  • I do not see why they answer my question.
    – joseabp91
    Dec 2 '18 at 19:40
















0















This question already has an answer here:




  • existence of complex structure in dimension 2

    1 answer



  • Why does every noncompact orientable surface have a complex structure?

    1 answer




Let $M$ be a $2$-dimensional orientable manifold. Is $M$ a Riemann surface? If it is true, how can I show it? Thank you very much.










share|cite|improve this question













marked as duplicate by Dietrich Burde, Eric Wofsey, Lord Shark the Unknown, amWhy, Robert Soupe Dec 3 '18 at 3:03


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.















  • It is a $1$-dimensional complex manifold (in complex sense).
    – joseabp91
    Dec 2 '18 at 19:27








  • 1




    See: math.stackexchange.com/a/907476/534616
    – K B Dave
    Dec 2 '18 at 19:27










  • Not quite a duplicate of that one because the surface isn't required to be compact
    – K B Dave
    Dec 2 '18 at 19:29










  • I do not see why they answer my question.
    – joseabp91
    Dec 2 '18 at 19:40














0












0








0








This question already has an answer here:




  • existence of complex structure in dimension 2

    1 answer



  • Why does every noncompact orientable surface have a complex structure?

    1 answer




Let $M$ be a $2$-dimensional orientable manifold. Is $M$ a Riemann surface? If it is true, how can I show it? Thank you very much.










share|cite|improve this question














This question already has an answer here:




  • existence of complex structure in dimension 2

    1 answer



  • Why does every noncompact orientable surface have a complex structure?

    1 answer




Let $M$ be a $2$-dimensional orientable manifold. Is $M$ a Riemann surface? If it is true, how can I show it? Thank you very much.





This question already has an answer here:




  • existence of complex structure in dimension 2

    1 answer



  • Why does every noncompact orientable surface have a complex structure?

    1 answer








riemann-surfaces






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share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Dec 2 '18 at 19:15









joseabp91

1,243411




1,243411




marked as duplicate by Dietrich Burde, Eric Wofsey, Lord Shark the Unknown, amWhy, Robert Soupe Dec 3 '18 at 3:03


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.






marked as duplicate by Dietrich Burde, Eric Wofsey, Lord Shark the Unknown, amWhy, Robert Soupe Dec 3 '18 at 3:03


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.














  • It is a $1$-dimensional complex manifold (in complex sense).
    – joseabp91
    Dec 2 '18 at 19:27








  • 1




    See: math.stackexchange.com/a/907476/534616
    – K B Dave
    Dec 2 '18 at 19:27










  • Not quite a duplicate of that one because the surface isn't required to be compact
    – K B Dave
    Dec 2 '18 at 19:29










  • I do not see why they answer my question.
    – joseabp91
    Dec 2 '18 at 19:40


















  • It is a $1$-dimensional complex manifold (in complex sense).
    – joseabp91
    Dec 2 '18 at 19:27








  • 1




    See: math.stackexchange.com/a/907476/534616
    – K B Dave
    Dec 2 '18 at 19:27










  • Not quite a duplicate of that one because the surface isn't required to be compact
    – K B Dave
    Dec 2 '18 at 19:29










  • I do not see why they answer my question.
    – joseabp91
    Dec 2 '18 at 19:40
















It is a $1$-dimensional complex manifold (in complex sense).
– joseabp91
Dec 2 '18 at 19:27






It is a $1$-dimensional complex manifold (in complex sense).
– joseabp91
Dec 2 '18 at 19:27






1




1




See: math.stackexchange.com/a/907476/534616
– K B Dave
Dec 2 '18 at 19:27




See: math.stackexchange.com/a/907476/534616
– K B Dave
Dec 2 '18 at 19:27












Not quite a duplicate of that one because the surface isn't required to be compact
– K B Dave
Dec 2 '18 at 19:29




Not quite a duplicate of that one because the surface isn't required to be compact
– K B Dave
Dec 2 '18 at 19:29












I do not see why they answer my question.
– joseabp91
Dec 2 '18 at 19:40




I do not see why they answer my question.
– joseabp91
Dec 2 '18 at 19:40










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