The intersection curve of two spacelike surfaces is a spacelike, the intersection curve of two timelike surfaces may be spacelike or timelike, the intersection curve of two lightlike surfaces may be spacelike or null, the intersection curve of spacelike and timelike surfaces is spacelike, the intersection curve of spacelike and lightlike surfaces is spacelike, and the intersection curve of timelike and lightlike surfaces spacelike or null. We obtain the transversal intersection case, when the normal vectors of the surfaces are linearly independent.
For what follows we suppose
be a transversal intersection curve of two
arbitrary surfaces
and
and assume that the
curve
is a regular curve
parametrized by a parameter with the same trace as the curve
. Let
and
denote the
normal vector fields of the surfaces and respectively. Also,
let
and
denote the unit normal vector
fields of the surfaces and respectively. Assume that
,
,
.
Since
is orthogonal to
and
so by using proposition 2, we obtain