Abstract:
In the work possible complexes of three-dimensional planes in six-measured projective space $\mathbf{P}^6$ are studied. It's proved that one-parametric family of cones of second order with three-dimensional flats forming and univariate top, which describes unfold surface defines four-parametric possible family of planes $E^3$, which are all three-dimensional forming to this cones.
It's also proved that if we take in space $\mathbf{P}^6$ four-parametric family of three-dimensional planes including fixed straight line $l$ and touching two hypercone with one general univariate top $l$ we will get possible family of three-dimensional planes. Corresponding family tangent of four-parametric family is formed by intersection of tangent hyperplanes to the cones in the sport of osculation of three- dimensional planes family with them.
Keywords:Six-measured projective space, family of cones of second order with three-dimensional flats forming.