Quantum Clifford algebra from classical differential geometry

2002 ◽  
Vol 43 (3) ◽  
pp. 1353-1364 ◽  
Author(s):  
Jose G. Vargas ◽  
Douglas G. Torr
Keyword(s):  
Differential Geometry ◽  
Clifford Algebra ◽  
Classical Differential Geometry ◽  
Quantum Clifford Algebra

scholarly journals Lectures on Classical Differential Geometry.

1952 ◽  
Vol 59 (2) ◽  
pp. 119 ◽  
Author(s):  
C. E. Springer ◽  
D. J. Struik
Keyword(s):  
Differential Geometry ◽  
Classical Differential Geometry

Topological constraints on solar loop plasma instabilities and Alfvén waves

Open Physics ◽  
2009 ◽  
Vol 7 (1) ◽  
Author(s):  
Luiz Garcia de Andrade
Keyword(s):  
Differential Geometry ◽  
Wave Propagation ◽  
Imaginary Axis ◽  
The Other ◽  
Alfven Wave ◽  
Normal Vector ◽  
Frenet Frame ◽  
Topological Constraints ◽  
Classical Differential Geometry ◽  
Solar Loops

AbstractInhomogeneous plasmas-solar instabilities-are investigated by using the techniques of classical differential geometry for curves, where the Frenet torsion and curvature describe completely the motion of a curve. In our case, the Frenet frame changes in time and also depends upon the other coordinates, taking into account the inhomogeneity of the plasma. The exponential perturbation method, so commonly used to describe cosmological perturbations, is applied to the magnetohydrodynamic (MHD) plasma equations to find modes describing Alfvén wave propagation in the medium of planar loops. Stability is investigated in the imaginary axis of the spectra of complex frequencies ω, i.e. $$ \Im $$ m (ω) ≠ 0. A pratical guide for experimental solar physicists is given by computing the twist of force-free solar loops, which generalizes the Parker formula relating the twist to the Frenet torsion. In our expression the twist of the solar loops also depends on the abnormality of the normal vector of the frame.

scholarly journals The Use of Authentic Scientific Texts in the Process of Teaching Students to Solve Tasks of Differential Geometry

2019 ◽  
Vol 22 (6) ◽  
pp. 601-608
Author(s):  
Инесса Васильевна Игнатушина
Keyword(s):  
Differential Geometry ◽  
Educational Strategy ◽  
Creative Activity ◽  
Scientific Texts ◽  
Scientific Text ◽  
Classical Differential Geometry ◽  
The Relationship

In the article presents the classification of problems by differential geometry, which is based on the nature of the relationship between the elements of the problem and the relationship between the reproducing and creative activity of students in their decision. It is shown that an important source for the choice of texts of problems and methods of their solution are the works of scientists – creators of classical differential geometry. Work with the corresponding scientific text allows the student to master such an educational strategy as methodological reduction.

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