On the geometry of the (2n+1)-webs in 2n-dimensional affinely connected spaces A2n

An approach for the investigation of the geometry of (2n+1) -webs in 2n-dimensional affinely connected spaces A_2n by means of the prolonged differentiation is given in 1] Using this approach in the present paper some properties of (2n+1)-webs in A_2n are studied. Necessary and sufficient conditions under which the generalized affinor of Hess of a (2n+1)-web is covariantly constant are found. The space A_2n, containing a (2n+1)-web with a constant covariant generalized affinor of Hess, is determined. Conditions for geodesicity of the lines of a given (2n+1)-web in A_2n in terms of its tensor are found, also.The present investigation is partially supported by the Ministry of Science and Higher Education of People's Republic of Bulgaria under grant 1021.