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We study stationary configurations mimicking nonholonomic locally anisotropicblack rings (for instance, with ellipsoidal polarizations and/or imbedded intosolitonic backgrounds) in three/six dimensional pseudo-Finsler/ Riemannianspacetimes. In the asymptotically flat limit, for holonomic configurations, asubclass of such spacetimes contains the set of five dimensional black ringsolutions with regular rotating event horizon. For correspondingparameterizations, the metrics and connections define Finsler-Einsteingeometries modeled on tangent bundles, or on nonholonomic (pseudo) Riemannianmanifolds. In general, there are vacuum nonholonomic gravitationalconfigurations which can not be generated in the limit of zero cosmologicalconstant.

Nonholonomic Black Ring and Solitonic Solutions in Finsler and Extra Dimension Gravity Theories