arXiv subjects

Raymond O. Wells Jr

Publications and source records attributed to Raymond O. Wells Jr.

5 recordsLinked to original sources

arXiv2018

Compact complex surfaces with no nonconstant meromorphic functions

In 1949 Siegel gave an example of a complex two-torus with no nonconstant meromorphic functions. In 1964 Kodaira showed that compact complex surfaces with no nonconstant meromorphic must be of the following three types: tori, Hopf type surfaces with first Betti number equal to one, and K3 surfaces. In this paper we show that surfaces of these three types have a dense set of surfaces in their natural moduli spaces with no nonconstant meromorphic functions.

math.CV↗

arXiv2016

The geometry of manifolds and the perception of space

This essay discusses the development of key geometric ideas in the 19th century which led to the formulation of the concept of an abstract manifold (which was not necessarily tied to an ambient Euclidean space) by Hermann Weyl in 1913. This notion of manifold and the geometric ideas which could be formulated and utilized in such a setting (measuring a distance between points, curvature and other geometric concepts) was an essential ingredient in Einstein's gravitational theory of space-time from 1916 and has played important roles in numerous other theories of nature ever since.

math.HO↗

arXiv2015

Geometry in the Age of Enlightenment

This paper describes the evolution of aspects of differential and algebraic gometry from the mid 17th century till the end of the 18th century.

math.HO↗

arXiv2015

The Origins of Complex Geometry in the 19th Century

This paper gives an overview of several key innovations in the 19th century which led to complex geometry in the 20th century. This includes the creation of the complex plane, the work of Abel on addition theorems for generalized elliptic integrals, the theory of elliptic functions, holomorphic functions, and the creation of Riemann surfaces by Riemann in the mid 19th century. A number of the original papers which contain these new ideas are looked at in some detail and a detailed set of references is included.

math.HO↗

arXiv2013

Key developments in geometry in the 19th Century

This paper describes several key discoveries in the 19th century that led to the modern theory of manifolds in the twentieth century: intrinsic differential geometry, projective geometry and higher dimensional manifolds and Riemannian geometry.

math.HO↗