Curvature forms for Lorentz $2$-manifolds

Algebras of Curvature Forms on Homogeneous Manifolds

Let C(X) be the algebra generated by the curvature two-forms of standard holomorphic hermitian line bundles over the complex homogeneous manifold X = G/B. The cohomology ring of X is a quotient of C(X). We calculate the Hilbert polynomial of this algebra. In particular, we show that the dimension of C(X) is equal to the number of independent subsets of roots in the corresponding root system. We...

On Stretch curvature of Finsler manifolds

In this paper, Finsler metrics with relatively non-negative (resp. non-positive), isotropic and constant stretch curvature are studied.  In particular, it is showed that every compact Finsler manifold with relatively non-positive (resp. non-negative) stretch curvature is a Landsberg metric. Also, it is proved that every  (α,β)-metric of non-zero constant flag curvature and non-zero relatively i...

P-forms and Ricci Flow with Bounded Curvature on Manifolds

In this paper, we study the evolution of L p-forms under Ricci flow with bounded curvature on a complete non-compact or a compact Riemannian manifold. We show that under curvature pinching conditions on such a manifold, the L norm of a smooth p-form is non-increasing along the Ricci flow. The L∞ norm is showed to have monotonicity property too.

Curvature Computations of 2-manifolds in IRk

Regularity for Lorentz Metrics under Curvature Bounds

Let (M, g) be an (n+1)-dimensional space time, with bounded curvature, with respect to a bounded framing. If (M, g) is vacuum, or satisfies a mild condition on the stress-energy tensor, then we show that (M, g) locally admits coordinate systems in which the Lorentz metric g is wellcontrolled in the (space-time) Sobolev space L, for any p <∞.