Differential algebra (contravariant analytic methods in differential geometry)

1980 ◽  
Vol 14 (3) ◽  
pp. 1177-1187 ◽  
Author(s):  
A. M. Vasil'ev
Keyword(s):  
Differential Geometry ◽  
Differential Algebra ◽  
Analytic Methods

Topics in Direct Differential Geometry

1972 ◽  
Vol 24 (1) ◽  
pp. 98-148 ◽  
Author(s):  
Ralph Park
Keyword(s):  
Differential Geometry ◽  
Geometric Theory ◽  
Central Projection ◽  
Analytic Methods ◽  
Geometric Methods ◽  
Osculating Spaces ◽  
The Subject

In the theory of curves, one often makes differentiability assumptions in order that analytic methods can be used. Then one tries to weaken these assumptions as much as possible. The theory of curves which is presented here uses geometric methods, such as central projection, rather than analysis. In this way, no analytic assumptions are needed and a purely geometric theory results. Since this theory is not so well known as the analytic one, I have tried to make the treatment as self-contained as possible. It is hoped that this paper will form a quick introduction for a reader who has had no previous acquaintance with the subject.We assume that our curves satisfy a condition, which we call direct differentiability. Roughly this condition is that, at each point of the curve, all the osculating spaces exist.

scholarly journals DIFFERENTIAL GEOMETRY OF THE q-PLANE

2000 ◽  
Vol 15 (20) ◽  
pp. 3237-3243
Author(s):  
SULTAN A. ÇELIK ◽  
SALIH ÇELIK
Keyword(s):  
Differential Geometry ◽  
Hopf Algebra ◽  
Differential Algebra ◽  
Algebra Structure ◽  
Hopf Algebra Structure

Hopf algebra structure on the differential algebra of the extended q-plane is defined. An algebra of forms which is obtained from the generators of the extended q-plane is introduced and its Hopf algebra structure is given.

Applicable Differential Geometry

1987 ◽  
Author(s):  
M. Crampin ◽  
F. A. E. Pirani
Keyword(s):  
Differential Geometry
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