Quadratic Lagrangians in a space with torsion

A general expression is given for a quadratic (with respect to the curvature tensor) Lagrangian in a space with torsion. The given formalism is discussed in application to generalized Einstein-Cartan gravitation theory and the theory of the spin gauge field introduced in localization of the tetrad Lorentz transformation group.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 7–10, December, 1977.The author is indebted to Prof. D. D. Ivanenko, V. N. Ponomarev, and P. L. Poznanin for a useful and stimulating discussion.