A method, due tó Elie Cartan, is used to give an algebraic classification of the non-reductive homogeneous pseudo-Riemannian manifolds of dimension four. Only one case with Lorentz signature can be Einstein without having constant curvature, and two cases with (2,2) signature are Einstein of which one is Ricci-flat. If a four-dimensional non-reductive homogeneous pseudo-Riemannian manifold is s...

Let V = R be the pseudo-Euclidean vector space of signature (p, q), p ≥ 3 and W a module over the even Clifford algebra Cl0(V ). A homogeneous quaternionic manifold (M,Q) is constructed for any spin(V )-equivariant linear map Π : ∧2W → V . If the skew symmetric vector valued bilinear form Π is nondegenerate then (M,Q) is endowed with a canonical pseudo-Riemannian metric g such that (M,Q, g) is ...

In terms of synthetic differential geometry, we give a variational characterization of the connection (parallelism) associated to a pseudo-Riemannian metric on a manifold.

in the first part of this paper, some theorems are given for a riemannian manifold with semi-symmetric metric connection. in the second part of it, some special vector fields, for example, torse-forming vector fields, recurrent vector fields and concurrent vector fields are examined in this manifold. we obtain some properties of this manifold having the vectors mentioned above.

In this paper, we first give a definition of pseudo-Riemannian quasi constant curvature manifold and then generalize T.Ishihara’s results. Mathematics Subject Classification: 53C42.

The number of functionally independent scalar invariants of arbitrary order of a generic pseudo–Riemannian metric on an n–dimensional manifold is determined.

In this paper we consider pseudo projectively flat Riemannian manifold whose Ricci tensor S satisfies the condition S(X,Y ) = rT (X)T (Y ), where r is the scalar curvature, T is a non-zero 1-form defined by g(X, ξ) = T (X), ξ is a unit vector field and prove that the manifold is of pseudo quasi constant curvature, integral curves of the vector field ξ are geodesic and ξ is a proper concircular ...

Abstract. The present paper discusses the question of formulating and solving minimal-distance problems over the group-manifold of real symplectic matrices. In order to tackle the related optimization problem, the real symplectic group is regarded as a pseudo-Riemannian manifold and a metric is chosen that affords the computation of geodesic arcs in closed forms. Then, the considered minimal-di...

In this paper we study the convergence of Riemannian submanifolds. In particular, we prove that any sequence of closed submanifolds with bounded normal curvature and volume in a closed Riemannian manifold subconverge to a closed submanifold in the C1 ,Q topology. We also obtain some applications to irreducible homogeneous manifolds and pseudo-holomorphic curves in symplectic manifolds.