Classification of ten-dimensional symmetric embeddings for the spatially flat Friedman model

All possible variants of symmetric embedding of the metric of the spatially flat Friedman model into a ten-dimensional ambient space are analyzed. It is shown that only two such embeddings exist: the five-dimensional embedding found by Robertson in 1933 and a new eight-dimensional embedding proposed in this work. The new embedding can be utilized in developing the idea of explaining dark matter as fictitious matter arising in the description of gravity within the embedding theory approach. Some results in this direction are presented. Additionally, the possibility of constructing embeddings of the spatially flat Friedman model whose symmetry is lower than that of the metric itself is discussed. Two such embeddings are constructed.