- #1
Bacle
- 662
- 1
Hi, Everyone:
I am trying to understand the meaning of a statement that two embedded manifolds
intersect normally*. The statement is made in a context in which any choice or existence
of a metric is not made explicit, nor--from what I can tell-- implicitly either.
If there was a choice of metric m, it seems reasonable to conclude that M,N
intersect normally if the tangent spaces at points of intersection are normal to
each other, i.e., if p is in the intersection, then TpM is orthogonal to TpN , with
respect to the metric given by m. Without a choice of m, it seems difficult to
see how to define normality of intersection. .
Is there then,a definition of normal intersection that does not make reference, or
does not make use of, the existence of a metric?
Thanks.
* More precisely, the statement is that M intersects N normally along DelM, the (manifold)
boundary of M
I am trying to understand the meaning of a statement that two embedded manifolds
intersect normally*. The statement is made in a context in which any choice or existence
of a metric is not made explicit, nor--from what I can tell-- implicitly either.
If there was a choice of metric m, it seems reasonable to conclude that M,N
intersect normally if the tangent spaces at points of intersection are normal to
each other, i.e., if p is in the intersection, then TpM is orthogonal to TpN , with
respect to the metric given by m. Without a choice of m, it seems difficult to
see how to define normality of intersection. .
Is there then,a definition of normal intersection that does not make reference, or
does not make use of, the existence of a metric?
Thanks.
* More precisely, the statement is that M intersects N normally along DelM, the (manifold)
boundary of M