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We argue that the Einstein gravity theory can be reformulated in almostKahler (nonsymmetric) variables with effective symplectic form and compatiblelinear connection uniquely defined by a (pseudo) Riemannian metric. A class ofnonsymmetric theories of gravitation (NGT) on manifolds enabled withnonholonomic distributions is analyzed. There are considered some conditionswhen the fundamental geometric and physical objects are determined/ modified bynonholonomic deformations in general relativity or by contributions from Ricciflow theory and/or quantum gravity. We prove that in such NGT, for certainclasses of nonholonomic constraints, there are modelled effective Lagrangianswhich do not develop instabilities. It is also elaborated a linearizationformalism for anholonomic NGT models and analyzed the stability of stationaryellipsoidal solutions defining some nonholonomic and/or nonsymmetricdeformations of the Schwarzschild metric. We show how to construct nonholonomicdistributions which remove instabilities in NGT. Finally we conclude thatinstabilities do not consist a general feature of theories of gravity withnonsymmetric metrics but a particular property of certain models and/or classesof unconstrained solutions.

Einstein Gravity in Almost Kahler Variables and Stability of Gravity with Nonholonomic Distributions and Nonsymmetric Metrics