Madjumdar-papapetrou Type Solutions in Sigma-model and Intersecting P-branes

The block-orthogonal generalization of the Madjumdar-Papapetrou type solutions for the σ model studied earlier are obtained and corresponding solutions with p -branes are considered. The existence of solutions and the number of independent harmonic functions is defined by the matrix of scalar products of vectors U s , governing the σ -model target space metric. For orthogonal U s , when target space is a symmetric homogeneous space, the solutions reduce to the previous ones. Two special classes of obtained solutions with U s related to finite dimensional Lie algebras and hyperbolic (Kac-Moody) algebras are singled out and investigated. The affine Cartan matrices do not arise in the scheme under consideration. Some examples of solutions and intersection rules for D = 11 supergravity, related D = 12 theory and extending them BD models are considered. For special multicenter solutions the indicators of horizon and curvature singularity are introduced.