Bochner techniques and cosmological models

We demonstrate the possibility of applying the Bochner techniques [R. Zh. Matematika, 2A, 746 (1985)] to dynamics of an ideal fluid in a curved space-time. One example of the result of such application is that every irrotational motion of cosmological fluid with zero expansion in a closed oriented space-time obeying the energy condition is shearless.Vladimir State Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 82–86, June, 1993.