scholarly journals Motion on constant curvature spaces and quantization using noether symmetries

2014 ◽  
Vol 24 (4) ◽  
pp. 043128
Author(s):  
Paul Bracken
Keyword(s):  
Constant Curvature ◽  
Noether Symmetries ◽  
Constant Curvature Spaces

scholarly journals Note on integrability of certain homogeneous Hamiltonian systems in 2D constant curvature spaces

2017 ◽  
Vol 381 (7) ◽  
pp. 725-732 ◽  
Author(s):  
Andrzej J. Maciejewski ◽  
Wojciech Szumiński ◽  
Maria Przybylska
Keyword(s):  
Hamiltonian Systems ◽  
Constant Curvature ◽  
Constant Curvature Spaces

scholarly journals Almost geodesic mappings of type π1* of spaces with affine connection

2021 ◽  
Vol 52 ◽  
pp. 30-36
Author(s):  
Volodymyr Evgenyevich Berezovskii ◽  
Josef Mikeš ◽  
Željko Radulović
Keyword(s):  
Constant Curvature ◽  
Affine Connection ◽  
Affine Connections ◽  
Fundamental Equations ◽  
Special Case ◽  
Constant Curvature Spaces

We consider almost geodesic mappings π1* of spaces with affine connections. This mappings are a special case of first type almost geodesic mappings. We have found the objects which are invariants of the mappings π1*. The fundamental equations of these mappings are in Cauchy form. We study π1* mappings of constant curvature spaces.

scholarly journals Noether Symmetries of the Area-Minimizing Lagrangian

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Adnan Aslam ◽  
Asghar Qadir
Keyword(s):  
Euclidean Space ◽  
Lie Algebra ◽  
Constant Curvature ◽  
Noether Symmetries ◽  
Zero Curvature ◽  
Space Of Constant Curvature ◽  
Area Minimizing

It is shown that the Lie algebra of Noether symmetries for the Lagrangian minimizing an(n-1)-area enclosing a constantn-volume in a Euclidean space isso(n)⊕sℝnand in a space of constant curvature the Lie algebra isso(n). Furthermore, if the space has one section of constant curvature of dimensionn1, another ofn2, and so on tonkand one of zero curvature of dimensionm, withn≥∑j=1knj+m(as some of the sections may have no symmetry), then the Lie algebra of Noether symmetries is⊕j=1kso(nj+1)⊕(so(m)⊕sℝm).

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