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I study transversal submanifolds,I have an example but I didn't find some quatities.

In Rn+p we consider the submanifold N=Rn+1, we know that P is tottaly geodesic and another manifolds M wich is the sphere of dimension n+1 of radius r and centrer p0. then the transversal intersection of M and P depend on the value of r. If the distance between N and p0 is less then r then M and N are transverse and the intersection is a sphere L of dimension n. in this situation I want to define the principale curvature of the inclusion L on M and the vector normal to L in M.

Another question for a normal vector to M (define below) in Rn+p how we can define the shape operator of the second fondamental form.

Thanks friends

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# Example of transversal submanifolds?

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