Riemannian submersions from almost contact metric manifolds

In this paper we obtain the structure equation of a contact-complex Riemannian submersion and give some applications of this equation in the study of almost cosymplectic manifolds with Kaehler fibres.Comment: Abh. Math. Semin. Univ. Hamb., to appea

G-structures and Domain Walls in Heterotic Theories

We consider heterotic string solutions based on a warped product of a four-dimensional domain wall and a six-dimensional internal manifold, preserving two supercharges. The constraints on the internal manifolds with SU(3) structure are derived. They are found to be generalized half-flat manifolds with a particular pattern of torsion classes and they include half-flat manifolds and Strominger's complex non-Kahler manifolds as special cases. We also verify that previous heterotic compactifications on half-flat mirror manifolds are based on this class of solutions.Comment: 29 pages, reference added, typos correcte

On paraquaternionic submersions between paraquaternionic K\"ahler manifolds

In this paper we deal with some properties of a class of semi-Riemannian submersions between manifolds endowed with paraquaternionic structures, proving a result of non-existence of paraquaternionic submersions between paraquaternionic K\"ahler non locally hyper paraK\"ahler manifolds. Then we examine, as an example, the canonical projection of the tangent bundle, endowed with the Sasaki metric, of an almost paraquaternionic Hermitian manifold.Comment: 13 pages, no figure

Curvature properties of ϕ\phi-null Osserman Lorentzian S\mathcal{S}-manifolds

We expound some results about the relationships between the Jacobi operators with respect to null vectors on a Lorentzian $\mathcal{S}$-manifold $M$ and the Jacobi operators with respect to particular spacelike unit vectors on $M$. We study the number of the eigenvalues of such operators in a $\phi$-null Osserman Lorentzian $\mathcal{S}$-manifold, under suitable assumptions on the dimension of the manifold. Then, we generalize a curvature characterization, previously obtained by the first author for Lorentzian $\phi$-null Osserman $\mathcal{S}$-manifolds with exactly two characteristic vector fields, to the case of those with an arbitrary number of characteristic vector fields.Comment: 15 pages; signs corrected on page 8, reference adde

Locally conformal C6-manifolds and generalized Sasakian-space-forms

An algebraic characterization of generalized Sasakian-space-forms is stated. Then, one studies the almost contact metric manifolds which are locally conformal to $C_6$-manifolds, simply called l.c. $C_6$-manifolds. In dimension 2n+1>=5, any of these manifolds turns out to be locally conformal cosymplectic or globally conformal to a Sasakian manifold. Curvature properties of l.c. $C_6$-manifolds are obtained, with particular attention to the k-nullity condition. This allows one to state a local classification theorem, in dimension 2n+1>=5, under the hypothesis of constant sectional curvature. Moreover, one proves that an l.c. $C_6$-manifold is a generalized Sasakian-space-form if and only if it satisfies the k-nullity condition and has pointwise constant $\varphi$-sectional curvature. Finally, local classification theorems for the generalized Sasakian-space-forms in the considered class are obtained

Curvature of Locally Conformal Cosymplectic Manifolds

Locally conformal cosymplectic manifolds are investigated from the point of view of the curvature. Particular attention to the N(k)-nullity condition is given and classification theorems in dimension 2n+1>=5 are stated. This also allows to classify locally conformal cosymplectic manifolds which are locally symmetric spaces