Differential geometry of surfaces in Euclidean space
... be parameterized by a set of m “curvilinear” coordinates, denoted using Greek indices, y µ ; the surface is defined by giving the Euclidean coordinates xA as a function of the curvilinear ones, xA = xA (~y ). In the special case m = n, this can be thought of as a formalism to deal with curvilinear c ...
... be parameterized by a set of m “curvilinear” coordinates, denoted using Greek indices, y µ ; the surface is defined by giving the Euclidean coordinates xA as a function of the curvilinear ones, xA = xA (~y ). In the special case m = n, this can be thought of as a formalism to deal with curvilinear c ...
On the average distance property of compact connected metric spaces
... A d d e d in p r o o f (2.2. 1983). Since this paper was written there has been considerable activity on this topic which is now known as "Numerical Geometry". (1) Professor Jan Mycielski has drawn our attention to the paper "The rendezvous value of a metric space" by O. Gross which appeared in Ann. ...
... A d d e d in p r o o f (2.2. 1983). Since this paper was written there has been considerable activity on this topic which is now known as "Numerical Geometry". (1) Professor Jan Mycielski has drawn our attention to the paper "The rendezvous value of a metric space" by O. Gross which appeared in Ann. ...
Riemann–Roch theorem
The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeroes and allowed poles. It relates the complex analysis of a connected compact Riemann surface with the surface's purely topological genus g, in a way that can be carried over into purely algebraic settings.Initially proved as Riemann's inequality by Riemann (1857), the theorem reached its definitive form for Riemann surfaces after work of Riemann's short-lived student Gustav Roch (1865). It was later generalized to algebraic curves, to higher-dimensional varieties and beyond.