Re: a problem of differential geometry

Hey guys, I read differential geometry by M.P.do Carmo.
In the sec1.5,
he wrote

It follows that a(s).b0 = constant(here, . means inner product); hence,
a(s) is contained in a plane normal to b0.

Why?
The product of a vector A and a constant vector B is a constant, then
will A lies in a plane normal to b0? In fact I know if their inner
product is zero, then A will lies in a plane normal to b0, but if the
product is not zero, will it?

As you state it, the conclusion is in fact not correct. But looking in my crystal ball, I guess that you didn't read it carefully; i.e. you missed a prime after a(s), meaning that a(s)' (the derivative vector of a(s) with respect to s) is in a plane normal to b0. Am I correct?
Ciao
Karl

.