- #1
- 7,319
- 11,152
Hi, All:
I need some help with some "technology" on differential forms, please:
1)Im trying to understand how the hyperplane field Tx[itex]\Sigma[/itex]<
TpM on M=[itex]\Sigma[/itex] x S1 , where [itex]\Sigma[/itex]
is a surface, is defined as the kernel of the form dθ (the top form on S1).
I know that T(x,y)(MxN)≈TxM(+)TyM
But this seems to bring up issues of the dual Tp*M,
i.e., the cotangent bundle of M .
How do we define a linear map on a sum vm+vn , each
a vector on the tangent spaces of M,N at x,y respectively? I think this may have
to see with the tensor product, but I'm not sure.
Thanks .
I need some help with some "technology" on differential forms, please:
1)Im trying to understand how the hyperplane field Tx[itex]\Sigma[/itex]<
TpM on M=[itex]\Sigma[/itex] x S1 , where [itex]\Sigma[/itex]
is a surface, is defined as the kernel of the form dθ (the top form on S1).
I know that T(x,y)(MxN)≈TxM(+)TyM
But this seems to bring up issues of the dual Tp*M,
i.e., the cotangent bundle of M .
How do we define a linear map on a sum vm+vn , each
a vector on the tangent spaces of M,N at x,y respectively? I think this may have
to see with the tensor product, but I'm not sure.
Thanks .