- #1

WWGD

Science Advisor

Gold Member

2019 Award

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I need some help with some "technology" on differential forms, please:

1)Im trying to understand how the hyperplane field T

_{x}[itex]\Sigma[/itex]<

T

_{p}M on M=[itex]\Sigma[/itex] x S

^{1}, where [itex]\Sigma[/itex]

is a surface, is defined as the kernel of the form dθ (the top form on S

^{1}).

I know that T

_{(x,y)}(MxN)≈T

_{x}M(+)T

_{y}M

But this seems to bring up issues of the dual T

_{p}

^{*}M,

i.e., the cotangent bundle of M .

How do we define a linear map on a sum v

_{m}+v

_{n}, 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 .