We investigate Kaluza-Klein metrics with a recurrent lightlike vector field over a pseudo-Riemannian manifold (B, g).

Following our approach to metric Lie algebras developed in a previous paper we propose a way of understanding pseudo-Riemannian symmetric spaces which are not semi-simple. We introduce cohomology sets (called quadratic cohomology) associated with orthogonal modules of Lie algebras with involution. Then we construct a functorial assignment which sends a pseudo-Riemannian symmetric space M to a t...

Almost all known restrictions on the topology of nonsingular real algebraic curves in the projective plane are also valid for a wider class of objects: real pseudo-holomorphic curves. It is still unknown if there exists a nonsingular real pseudo-holomorphic curve not isotopic in the projective plane to a real algebraic curve of the same degree. In this article, we focus our study on symmetric r...

We have studied some geometric properties of conharmonically flat Sasakian manifold and an Einstein-Sasakian manifold satisfying R(X, Y ).N = 0. We have also obtained some results on special weakly Ricci symmetric Sasakian manifold and have shown that it is an Einstein manifold. AMS Mathematics Subject Classification (2000): 53C21, 53C25

Let L ⊂ V = R be a maximally isotropic subspace. It is shown that any simply connected Lie group with a bi-invariant flat pseudo-Riemannian metric of signature (k, l) is 2-step nilpotent and is defined by an element η ∈ Λ3L ⊂ Λ3V . If η is of type (3, 0)+(0, 3) with respect to a skew-symmetric endomorphism J with J2 = ǫId, then the Lie group L(η) is endowed with a left-invariant nearly Kähler s...

Let M be a smooth manifold of positive dimension n equipped with a smooth density dμM. Let A be a polyhomogeneous elliptic pseudo-differential operator of positive order m onM which is symmetric for the L scalar product defined by dμM. For each L > 0, the space UL = ⊕ λ≤LKer(A− λId) is a finite dimensional subspace of C∞(M). Let ΠL be the spectral projector onto UL. Given s ∈ R, we compute the ...

In this paper we study the scalar geometries occurring in the dimensional reduction of minimal five-dimensional supergravity to three Euclidean dimensions, and find that these depend on whether one first reduces over space or over time. In both cases the scalar manifold of the reduced theory is described as an eight-dimensional Lie group L (the Iwasawa subgroup of G2(2)) with a left-invariant p...

We first derive the relation between the eikonal approximation to the Maxwell wave equations in an inhomogeneous anisotropic medium and geodesic motion in a three dimensional Riemannian manifold using a method which identifies the symplectic structure of the corresponding mechanics. We then apply an analogous method to the five dimensional generalization of Maxwell theory required by the gauge ...

We examine the properties and consequences of pseudo-supersymmetry for quantum systems admitting a pseudo-Hermitian Hamiltonian. We explore the Witten index of pseudo-supersymmetry and show that every pair of diagonalizable (not necessarily Hermitian) Hamiltonians with discrete spectra and real or complex-conjugate pairs of eigenvalues are isospectral and have identical degeneracy structure exc...