Dec 22 2023

## k-planes

As presented before, a magnetic field can bend a charge path, but not speed it up or slow it down. k-planes are produced by magnetic fields, whereby they manipulate the direction of electric fields. Due to a charged mass, k-planes are produced, and this means that electric fields of gravitons are bent into the same plane as the vector potential comes through. A vector potential can be a charged mass or a group traveling through the gamma ray field before acting on another charge.

When two graviton electric fields are combined it is called a “k-th Chern class ck(E)” ([1], pg. 309) and a “2k form γk“. When a “4k-form βk” ([1], pg. 309), it is called a “Pontrjagin class”. We may think of a Pontrjagin class as a flat picture of a mountain range with 4 mountains in the picture. It is not a sine or cosine curve, but has 4 lobes. The curve that defines the tops of the mountains can be thought of as a string. Statistically, lobes may be combined at times. There are “two elements (A, p) and (B, q)” ([2], pg. 216), and q is the distance the p moves laterally to help form a hypersurface k-plane. For example, there is a “2k-form on P” ([1], pg. 293) for a Chern class, and in any k class there is “oriented p-planes in Rp+q” ([1], pg. 271).

k-planes are created to do heavy work, and are parts of larger Lie groups which determine the chirality. As the group approaches another charge, it determines whether the charge is positive or negative. If it is of the same charge sign, the Lie groups instruct the k-planes to slap the target charge on the face. If the target is the opposite charge sign, the k-planes split, spin around, and slap the target charge on the back. After 18 years, we really need the String Theorists working on the mathematics of this.

The k-planes take up new gravitons quickly and leave others behind. It is its own entity within a Lie group, and “(g, h, σ) is effective” ([1], pg. 249), σ being the effect of the magnetic field.

[1] Kobayashi, Shoshichi and Nomizu, Katsumi, “Foundations of Differential Geometry Volume II”, John Wiley & Sons, Inc., c. 1969

[2] Kobayashi, Shoshichi and Nomizu, Katsumi, “Foundations of Differential Geometry Volume I”, John Wiley & Sons, Inc., c. 1963