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If we define the derivatives of T, N, and n as the following

[itex]T'=-k_{g}n+k_{n}N[/itex]

[itex]n'=k_{g}T+\tau_{g}N[/itex]

[itex]N'=-k_{n}T-\tau_{g}n[/itex]

then we should have [itex]N'\cdot T = -k_{n}[/itex] and the second fundamental form is given by [itex]II(T,T) = k_{n}[/itex] while [itex]N'\cdot n=-\tau_{g}[/itex] so that the second fundamental form is given by [itex]II(T,n)=\tau_{g}[/itex].

This seems pretty clear to me, unless I have my definitions mixed up some how. Does this seem correct?