INTRODUCTION TO DIFFERENTIAL GEOMETRY AND RIEMANNIAN GEOMETRY

1970 ◽  
Vol 2 (2) ◽  
pp. 243-244
Author(s):  
R. S. Clark
Keyword(s):  
Differential Geometry ◽  
Riemannian Geometry

A Generalization of Finsler Geometry

1962 ◽  
Vol 14 ◽  
pp. 87-112 ◽  
Author(s):  
J. R. Vanstone
Keyword(s):  
Differential Geometry ◽  
General Theory ◽  
Distance Function ◽  
Riemannian Geometry ◽  
Finsler Geometry ◽  
Riemannian Metric ◽  
Elliptic Partial Differential Equations ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Metric Function

Modern differential geometry may be said to date from Riemann's famous lecture of 1854 (9), in which a distance function of the form F(xi, dxi) = (γij(x)dxidxj½ was proposed. The applications of the consequent geometry were many and varied. Examples are Synge's geometrization of mechanics (15), Riesz’ approach to linear elliptic partial differential equations (10), and the well-known general theory of relativity of Einstein.Meanwhile the results of Caratheodory (4) in the calculus of variations led Finsler in 1918 to introduce a generalization of the Riemannian metric function (6). The geometry which arose was more fully developed by Berwald (2) and Synge (14) about 1925 and later by Cartan (5), Busemann, and Rund. It was then possible to extend the applications of Riemannian geometry.

scholarly journals Arthur Geoffrey Walker. 17 July 1909 — 31 March 2001

2006 ◽  
Vol 52 ◽  
pp. 413-421
Author(s):  
Nigel J. Hitchin
Keyword(s):  
Differential Geometry ◽  
Quantum Theory ◽  
Riemannian Geometry ◽  
Psychiatric Illness ◽  
Grammar School ◽  
Atomic Spectra ◽  
King's College

Arthur Geoffrey Walker was born in Watford, Hertfordshire, on 17 July 1909, and attended Watford Grammar School, from where he won in 1928 an Open Mathematical Scholarship to Balliol College, Oxford. There, his tutor was John William Nicholson FRS, who had been a professor at King's College, London, and was one of the first mathematical physicists to relate quantum theory to atomic spectra. However, in the late 1920s he was suffering from a psychiatric illness and in 1930 was hospitalized, so that Walker had to study on his own a great deal. This perhaps influenced his subsequent method of working on mathematics, which he normally did in the privacy of his room rather than in active consultation with others. He obtained a Second in Moderations, but in 1930 won a Junior Mathematical Exhibition and in 1931 took a First with a Distinction in the special subject of differential geometry, which was to become his life's work. Eisenhart's book Riemannian geometry (Eisenhart 1926) became his bible and he continually referred to it in many of his papers.

scholarly journals A Survey on Differential Geometry of Riemannian Maps Between

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
Bayram Şahin
Keyword(s):  
Differential Geometry ◽  
Riemannian Manifolds ◽  
Riemannian Geometry ◽  
Research Area ◽  
Riemannian Submersions ◽  
Open Problems ◽  
Geometric Objects ◽  
Riemannian Map

AbstractThe main aim of this paper is to state recent results in Riemannian geometry obtained by the existence of a Riemannian map between Riemannian manifolds and to introduce certain geometric objects along such maps which allow one to use the techniques of submanifolds or Riemannian submersions for Riemannian maps. The paper also contains several open problems related to the research area.

scholarly journals Riemannian Geometry and Modern Developments

2019 ◽  
Vol 39 ◽  
pp. 71-85
Author(s):  
AKM Nazimuddin ◽  
Md Showkat Ali
Keyword(s):  
Differential Geometry ◽  
Scalar Curvature ◽  
Constant Curvature ◽  
Riemannian Geometry ◽  
Ricci Tensor ◽  
Software Tool ◽  
3 Dimensional ◽  
Christoffel Symbols ◽  
Implementation Method

In this paper, we compute the Christoffel Symbols of the first kind, Christoffel Symbols of the second kind, Geodesics, Riemann Christoffel tensor, Ricci tensor and Scalar curvature from a metric which plays a fundamental role in the Riemannian geometry and modern differential geometry, where we consider MATLAB as a software tool for this implementation method. Also we have shown that, locally, any Riemannian 3-dimensional metric can be deformed along a directioninto another metricthat is conformal to a metric of constant curvature GANIT J. Bangladesh Math. Soc.Vol. 39 (2019) 71-85

scholarly journals Psychology and geometry: I. On the geometry of the human kind

Filomat ◽  
2015 ◽  
Vol 29 (3) ◽  
pp. 545-552
Author(s):  
Leopold Verstraelena
Keyword(s):  
Differential Geometry ◽  
Riemannian Geometry ◽  
Point Of View ◽  
Psychological Point ◽  
History Of ◽  
Present Part ◽  
Human Kind

In this note an attempt is made to describe a personal look at some of the main steps in the history of geometry from a psychological point of view, hereby basing on and sometimes merely formulating again parts of some previous papers, like [1-11]. For general references on elementary differential geometry, pseudo Riemannian geometry and geometry of submanifolds, see e.g. [12-22]. In reference [23], part II of some of the author?s reflections on psychology and geometry, an attempt is made to describe relativistic spacetimes in a way as kind of a supplement to the contents of the present part I.

Introduction to Differential Geometry and Riemannian Geometry

1970 ◽  
Vol 54 (388) ◽  
pp. 193 ◽  
Author(s):  
T. J. Willmore ◽  
Erwin Kreyszig
Keyword(s):  
Differential Geometry ◽  
Riemannian Geometry
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