The curvature theory of strongly distinguished connection in the recurrent \(K\)-Hamilton space (Q1194633)

The authoress considers a \(k\)-Hamilton space \(E^*\), a Riemannian structure \(G\) on \(E^*\), the vertical bundle \(T_ v(E^*)\) with respect to a projection \(\pi^*: E^*\to M\) and the orthogonal supplement \(T_ H(E^*)\) of \(T_ V(E^*)\) with respect to \(G\). The tangent bundle \(T(E^*)\) admits a decomposition \[ T(E^*)=T_ H(E^*)\oplus_{(1)}T_ V(E^*)\oplus \dots \oplus_{(k)}T_ V(E^*). \] A linear connection \(\nabla\) on \(E^*\) compatible with the above decomposition is called a strongly distinguished connection. The authoress studies the case when a strongly distinguished connection \(\nabla\) is recurrent with respect to \(G\). The torsion, curvature, Ricci and Bianchi identities for \(\nabla\) are studied, too.