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On geometry of transsymmetric spaces. (English) Zbl 0746.53051
Webs and quasigroups. (“Nonlinear geometric algebra-89”), Tver’, 117-122 (1991).
[For the entire collection see Zbl 0742.00044.]
Let \(M\) be a \(C^ \infty\)-manifold, \(\{S_ x\}\), \(x\in M\), be a family of local diffeomorphisms on \(M\). Then \((M,\{S_ x\})\) is said to be a transsymmetric space. Ts-spaces are the generalization of the well-known symmetric spaces and \(S\)-spaces. A reductive canonical affine connection \(\nabla\) is determined on a Ts-space. Some properties of \(\nabla\) are investigated.

MSC:
53C99 Global differential geometry
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