Compact conformal manifolds

Conformal mappings preserving the Einstein tensor of Weyl manifolds

In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...

Conformal connections on Lyra manifolds

We give an algebraic characterization of the case when conformal Weyl and conformal Lyra connections have the same curvature tensor. It is determined a (1,3)-tensor field invariant to certain transformation of semi-symmetric connections, compatible with Weyl structures on conformal manifolds. It is studied the case when this tensor is vanishing. M.S.C. 2000: 53B05, 53B20, 53B21.

Completeness of Compact Lorentz Manifolds Admitting a Timelike Conformal Killing Vector Field

It is proved that every compact Lorentz manifold admitting a timelike conformai Killing vector field is geodesically complete. So, a recent result by Kamishima in J. Differential Geometry [37 (1993), 569-601] is widely extended. Recently, it has been proved in [2] that a compact Lorentz manifold of constant curvature admitting a timelike Killing vector field is (geodesically) complete. It is na...

Surgery on Compact Manifolds

Flavordynamics with Conformal Matter and Gauge Theories on Compact Hyperbolic Manifolds in Extra Dimensions

We outline a toy model in which a unique mechanism may trigger a dynamical chain resulting in key low-energy regularities. The starting points are a negative cosmological term in the bulk and conformally invariant nongravity sector. These elements ensure compactification of the extra dimensional space on a compact hyperbolic manifold (with the negative and constant scalar curvature). The overal...