Lovelock’s theorem revisited
نویسندگان
چکیده
Let (X, g) be an arbitrary pseudo-riemannian manifold. A celebrated result by Lovelock ([4], [5], [6]) gives an explicit description of all second-order natural (0,2)-tensors on X, that satisfy the conditions of being symmetric and divergence-free. Apart from the dual metric, the Einstein tensor of g is the simplest example. In this paper, we give a short and self-contained proof of this theorem, simplifying the existing one by formalizing the notion of derivative of a natural tensor.
منابع مشابه
Kellerer’s theorem revisited
Kellerer’s theorem asserts the existence of a Markovian martingale with given marginals, assumed to increase in the convex order. It is revisited here, in the light of previous papers by Hirsch-Roynette and by G.Lowther.
متن کاملCholera Bacteriophages Revisited
123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012123 123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012123 123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012123 1234567890123456789012345678901212345678901234567890123456789012123456789012345678901234567890121...
متن کاملKolmogorov Theorem Revisited
Kolmogorov Theorem on the persistence of invariant tori of real analytic Hamiltonian systems is revisited. In this paper we are mainly concerned with the lower bound on the constant of the Diophantine condition required by the theorem. From the existing proofs in the literature, this lower bound turns to be ofO(ε1/4), where ε is the size of the perturbation. In this paper, by means of careful (...
متن کامل