On the manifold M(M) of all Riemannian metrics on a compact manifold M one can consider the natural L-metric as decribed first by [10]. In this paper we consider variants of this metric which in general are of higher order. We derive the geodesic equations, we show that they are well-posed under some conditions and induce a locally diffeomorphic geodesic exponential mapping. We give a condition...

In the present paper, the nonlinear equations describing all the nonsingular pencils of metrics of constant Riemannian curvature are derived and the integrability of these nonlinear equations by the method of inverse scattering problem is proved. These results were announced in our previous paper [1]. For the flat pencils of metrics the corresponding statements and proofs were presented in the ...

We consider variational inequality problems for set-valued vector fields on general Riemannian manifolds. The existence results of the solution, convexity of the solution set, and the convergence property of the proximal point algorithm for the variational inequality problems for set-valued mappings on Riemannian manifolds are established. Applications to convex optimization problems on Riemann...

The paper deals with twistor spinors on Lorentzian manifolds. In particular , we explain a relation between a certain class of Lorentzian twistor spinors and the Feeerman spaces of strictly pseudoconvex spin manifolds which appear in CR-geometry. Let (M n;k ; g) be a n-dimensional smooth semi-Riemannian spin manifold of index k with the spinor bundle S. There are two conformally covariant diffe...

As is well known, a metric on a manifold determines a unique symmetric connection for which the metric is parallel: the Levi-Civita connection. In this paper we investigate the inverse problem: to what extent is the metric of a Riemannian manifold determined by its LeviCivita connection? It is shown that for a generic Levi-Civita connection of a metric h there exists a set of positive semi-defi...

In this paper, notions of compatible and almost compatible Riemannian and pseudo-Riemannian metrics, which are motivated by the theory of compatible (local and nonlocal) Poisson structures of hydrodynamic type and generalize the notion of flat pencil of metrics (this notion plays an important role in the theory of integrable systems of hydrodynamic type and the Dubrovin theory of Frobenius mani...

We determine the limit of the bottom of spectrum of Schrödinger operators with variable coefficients on Wiener spaces and path spaces over finite dimensional compact Riemannian manifolds under semi-classical limit. These are extensions of the results in [4]. The problem on path spaces over Riemannian manifolds are considered as a problem on Wiener spaces by Ito’s map. However the coefficient op...

We classify the paracontact Riemannian manifolds that their Riemannian curvature satisfies in the certain condition and we show that this classification is hold for the special cases semi-symmetric and locally symmetric spaces. Finally we study paracontact Riemannian manifolds satisfying R(X, ξ).S = 0, where S is the Ricci tensor.