## Bimetric physical structures of rank $$(n+1,2)$$.(English. Russian original)Zbl 0828.53045

Sib. Math. J. 34, No. 3, 513-522 (1993); translation from Sib. Mat. Zh. 34, No. 3, 132-143 (1993).
The author gives a concise definition of an $$s$$-metric physical structure of rank $$(n + 1, m + 1)$$ where $$s \geq 1$$ and $$n \geq m \geq 1$$ are integer numbers. This is a kind of smooth and nondegenerate $$s$$-compact real function defined on an open dense subset in $${\mathfrak m} \times {\mathfrak n}$$ where $$\mathfrak m$$ and $$\mathfrak n$$ are smooth manifolds of dimensions $$sm$$ and $$sn$$, respectively. The author completes the classification of bimetric physical structures of rank $$(n + 1, 2)$$, $$n \geq 1$$, the case of a 2-dimensional manifold $$\mathfrak m$$ and a $$2n$$-dimensional manifold $$\mathfrak n$$, i.e. the case $$s =2$$ and $$m = 1$$, by using an old theorem of S. Lie obtained in 1883.

### MSC:

 53C30 Differential geometry of homogeneous manifolds 22E15 General properties and structure of real Lie groups 70A05 Axiomatics, foundations