The paper presents a geometric duality between the spherical squared-Hellinger distance and a hyperbolic isometric invariant of the Poincare disc under the action of the general Mobius group. Motivated by the geometric connection, we propose the usage of the L2-embedded hyperbolic isometric invariant as an alternative way to quantify divergence between Gaussian measures as a contribution to information theory.

翻译：本文揭示了球面平方Hellinger距离与一般莫比乌斯群作用下双曲圆盘的双曲等距不变量之间的几何对偶关系。基于这一几何关联，我们提出采用L2嵌入的双曲等距不变量作为量化高斯测度间散度的替代方法，以此作为对信息论领域的贡献。