No, the maximum and minimum values of non-normal curvature are not necessarily perpendicular to each other if the maximum and minimum values of normal curvature are perpendicular.
To understand this, let's clarify the concepts of normal curvature and non-normal curvature. Normal curvature refers to the curvature of a curve or surface in the direction of its normal vector. It measures how the curve or surface curves locally in the direction perpendicular to itself.
Non-normal curvature, on the other hand, refers to the curvature of a curve or surface in a direction that is not necessarily perpendicular to the surface. It can be measured in any direction, not limited to the normal direction.
If the maximum and minimum values of normal curvature are perpendicular, it means that the curve or surface has reached maximum curvature in one direction and minimum curvature in a direction perpendicular to it. However, this does not imply anything about the relationship between the maximum and minimum values of non-normal curvature.
In general, the values of non-normal curvature can be different in different directions and are not constrained to be perpendicular to each other. The behavior of non-normal curvature depends on the specific shape and geometry of the curve or surface, and it can vary independently of the normal curvature.
Therefore, the perpendicularity of the maximum and minimum values of normal curvature does not provide information about the relationship between the maximum and minimum values of non-normal curvature.