  In isotropic macroscopic quantum systems vortex lines can be formed while in
anisotropic systems also vortex sheets are possible. Based on measurements of
superfluid 3He-A, we present the principles which select between these two
competing forms of quantized vorticity: sheets displace lines if the frequency
of the external field exceeds a critical limit. The resulting topologically
stable state consists of multiple vortex sheets and has much faster dynamics
than the state with vortex lines.
