Compact Six-Dimensional Kähler Spin Manifolds of Positive Scalar Curvature with the Smallest Possible First Eigenvalue of the Dirac Operator.
A new class of -dimensional Lorentz spaces of index is introduced which satisfies some geometric conditions and can be regarded as a generalization of Lorentz space form. Then, the compact space-like hypersurface with constant scalar curvature of this spaces is investigated and a gap theorem for the hypersurface is obtained.
In this manuscript we provide new extensions for the Myers theorem in weighted Riemannian and Lorentzian manifolds. As application we obtain a closure theorem for spatial hypersurfaces immersed in some time-like manifolds.
We study local equivalence of left-invariant metrics with the same curvature on Lie groups and of dimension three, when is unimodular and is non-unimodular.