For any relatively minimal hyperelliptic fibration f with slope four, there exists the inequality with respect to the relative Euler-Poincaré characteristic X(f) of f and the genus g(f) of a fiber of ...

Abstract: I discuss the Euler-Poincar’e equation as described in Poincaré’s original paper. I consider, then, Lagrangian systems with lot of symmetries, and for which this equation simplifies. Typical ...

Euler’s identity is an equality found in mathematics that has been compared to a Shakespearean sonnet and described as "the most beautiful equation." It is a special case of a foundational equation in ...

Motivated by registration problems, this paper deals with a curve matching problem in homogeneous spaces. Let G be a connected finite-dimensional bi-invariant Lie group and K a closed subgroup. A ...