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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