Generalized symmetric submanifolds of Euclidean spaces (Q1819750)

This paper contains some results from the thesis written by the second author under the supervision of the first one. They study the so-called k-symmetric spaces, a class of Riemannian manifolds which generalizes properly the class of symmetric spaces. More precisely, the authors treat the following problem: which of the k-symmetric spaces can be realized as a k-symmetric submanifold in some \(E^ d ?\) (The notion of a ''realization'' has a specific meaning.) First they prove that each compact k-symmetric space has such a realization and they provide some nice examples. Then they derive some sufficient conditions for the non-compact case to be non-realizable. They derive several interesting conclusions from it and apply the theory for dimensions \(\leq 5\) to get an almost complete answer to the problem.