The sphere $S^2$ is not a totally real submanifold of $mathbb CP^2$












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So as the title says; Why the sphere $S^2$ can't be embedded as a totally real submanifod of $mathbb CP^2$? I asked a similar question about totally real submanifolds. e.g see Totally real submanifold of 2 dimensional complex manifold



Number 3 of the answer mentions the proof of $S^2$ being Lagrangian. But if $S^2$ is Lagrangian in $mathbb CP^2$ then it follows that $S^2$ is a totally real submanifold! Is it actually?






differential-geometry manifolds







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    2














    So as the title says; Why the sphere $S^2$ can't be embedded as a totally real submanifod of $mathbb CP^2$? I asked a similar question about totally real submanifolds. e.g see Totally real submanifold of 2 dimensional complex manifold



    Number 3 of the answer mentions the proof of $S^2$ being Lagrangian. But if $S^2$ is Lagrangian in $mathbb CP^2$ then it follows that $S^2$ is a totally real submanifold! Is it actually?






    differential-geometry manifolds







    share|cite|improve this question



























      2












      2








      2


      3





      So as the title says; Why the sphere $S^2$ can't be embedded as a totally real submanifod of $mathbb CP^2$? I asked a similar question about totally real submanifolds. e.g see Totally real submanifold of 2 dimensional complex manifold



      Number 3 of the answer mentions the proof of $S^2$ being Lagrangian. But if $S^2$ is Lagrangian in $mathbb CP^2$ then it follows that $S^2$ is a totally real submanifold! Is it actually?






      differential-geometry manifolds







      share|cite|improve this question















      So as the title says; Why the sphere $S^2$ can't be embedded as a totally real submanifod of $mathbb CP^2$? I asked a similar question about totally real submanifolds. e.g see Totally real submanifold of 2 dimensional complex manifold



      Number 3 of the answer mentions the proof of $S^2$ being Lagrangian. But if $S^2$ is Lagrangian in $mathbb CP^2$ then it follows that $S^2$ is a totally real submanifold! Is it actually?






      differential-geometry manifolds




      differential-geometry manifolds






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Nov 20 '18 at 23:39









      Bernard

      118k639112




      118k639112










      asked Nov 20 '18 at 23:34









      Amrat A

      31818




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