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.


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