The Construction Of λ₂-eigenmap Between S⁴→Sⁿ

The result aboutλ2-eigenmaps between spheres is nearly perfect on5 Sn,n≥5, but for n=4, the situation has not been researched yet. Let Sm-1 be the unit sphere of the Euclidean spaceRm. This paper mainly discuss the value of n in g:S4→Sn.The method is:for all the value about the basis on R5,while S4(?)R5, according to the sum of the square of the basis of Rn+1 (while Sn(?)Rn+1)is equal to one, we can get a matrix, from which we can get the conclusion: the range of the rank of the matrix,which is the value of...