On the automormphism group of a second order structure (Q1864683)

In this paper the author studies some properties of the automorphism group of special second order structures which are associated to semisimple flat homogeneous spaces. His main result is the following. Let \(M=G/K\) be a reductive homogeneous space and let \(Q\) be a second order structure, i.e. a subbundle of the 2-frame bundle \(P^2 (M)\) over \(M\), which is associated to a semisimple flat homogeneous space \(L/L_0\) where \((L,L_0)\) belongs to a certain table determined by \textit{T. Ochiai} [Trans. Am. Math. Soc. 152, 159-193 (1970; Zbl 0205.26004)]. If \(G\) acts as an automorphism group of \(Q\), then there exists a \(G\)-invariant torsion-free affine connection \(\Gamma\) belonging to \(Q\).