Information geometry is the differential geometric treatment of statistical models. It thereby
provides the mathematical foundation of statistics. Information geometry therefore is of …

Submanifold theory has emerged as a natural development of the classical study of curves
and surfaces in Euclidean three space with the methods of differential calculus. In the last …

We consider proposals for the cost of holographic path integrals. Gravitational path integrals
within finite radial cutoff surfaces have a precise map to path integrals in $ T\overline {T} …

Geometric, algebraic, and analytic descendants of Nash isometric embedding theorems Page
1 BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 54 …

Le 28 août 1878,a l'occasion de la septieme réuniona Paris de l'Association pour
l'Avancement de la Science, PL Tchebychev fit une conférence portant le même titre que cet …

The aim of this book is to reveal the potential of Lobachevsky's geometry in the context of its
emergence in various branches of current interest in contemporary science, first and …

We investigate the validity of the isometry extension property for (Riemannian) Einstein
metrics on compact manifolds M with boundary∂ M. Given a metric γ on∂ M, this is the …

We produce a new general family of flat tori in\mathbb R^ 4, the first one since Bianchi's
classical works in the nineteenth century. To construct these flat tori, obtained via small …

Let be the n-dimensional pseudo-Euclidean space of index p and M (n, p) the group of all
transformations of generated by pseudo-orthogonal transformations and parallel …

The structure of surfaces of revolution with constant Gaussian curvature in the Euclidean
space E3 is well known. From the fact that the induced metric is a metric of revolution it does …