ON CURVATURE AND EULER-POINCARE CHARACTERISTIC

On Curvature and Euler-poincare Characteristic.

Complex Projective Threefolds with Non-negative Canonical Euler-poincare Characteristic

Let V be a smooth complex projective 3-fold of general type with χ(ωV ) ≥ 0. We prove that the m-canonical map Φ|mKV | is birational onto its image for all m ≥ 14. Known examples show that the numerical bound r3 = 14 is optimal.

Weyl Curvature and the Euler Characteristic in Dimension Four

We give lower bounds, in terms of the Euler characteristic, for the L-norm of the Weyl curvature of closed Riemannian 4-manifolds. The same bounds were obtained by Gursky, in the case of positive scalar curvature metrics.

The Euler-Poincare theory of Metamorphosis

In the pattern matching approach to imaging science, the process of “metamorphosis” is template matching with dynamical templates (Trouvé and Younes, Found. Comp. Math., 2005). Here, we recast the metamorphosis equations of that paper into the Euler-Poincaré variational framework of Holm, Marsden, and Ratiu, Adv. in Math., 1998 and show that the metamorphosis equations contain the equations for...

Exponentiation and Euler Characteristic