Isometric embeddings of real projective spaces into Euclidean spaces

This paper studies isometric embeddings of RPnRPn via non-degenerate symmetric bilinear maps. The main result shows the infimum dimension of target Euclidean spaces among these constructions for RPnRPn is 12n(n+3). Next, we construct Veronese maps by induction, which realize the infimum. Finally, we give a simple proof of Rigidity Theorem of Veronese maps.