How can one generalize the Gauss map to higher dimensions? More specifically, bi-dimensional manifolds in $mathbbR^4$

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It's easy to define the unitary tangent fields of a $2$-dimensional surface $S: I times J to mathbbR^4$, but since I don't have the cross product anymore, an unitary normal field is harder to find.




geometry differential-geometry riemannian-geometry surfaces




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    It's easy to define the unitary tangent fields of a $2$-dimensional surface $S: I times J to mathbbR^4$, but since I don't have the cross product anymore, an unitary normal field is harder to find.




    geometry differential-geometry riemannian-geometry surfaces




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      It's easy to define the unitary tangent fields of a $2$-dimensional surface $S: I times J to mathbbR^4$, but since I don't have the cross product anymore, an unitary normal field is harder to find.




      geometry differential-geometry riemannian-geometry surfaces




      share|cite|improve this question













      It's easy to define the unitary tangent fields of a $2$-dimensional surface $S: I times J to mathbbR^4$, but since I don't have the cross product anymore, an unitary normal field is harder to find.





      geometry differential-geometry riemannian-geometry surfaces





      share|cite|improve this question












      share|cite|improve this question




      share|cite|improve this question








      edited Aug 1 at 21:34
























      asked Aug 1 at 21:16









      Matheus Andrade

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