scholarly journals Fundamental Solutions and Gegenbauer Expansions of Helmholtz Operators in Riemannian Spaces of Constant Curvature

2018 ◽  
Author(s):  
Howard S. Cohl ◽  
◽  
Thinh H. Dang ◽  
T.M. Dunster ◽  
◽  
...  
Keyword(s):  
Constant Curvature ◽  
Fundamental Solutions ◽  
Spaces Of Constant Curvature ◽  
Helmholtz Operators ◽  
Riemannian Spaces

scholarly journals Special semi-reducible pseudo-Riemannian spaces

2021 ◽  
Vol 14 (1) ◽  
pp. 48-59
Author(s):  
Юлія Степанівна Федченко ◽  
Олександр Васильович Лесечко
Keyword(s):  
Constant Curvature ◽  
Symmetric Spaces ◽  
Necessary Conditions ◽  
Conformally Flat ◽  
Spaces Of Constant Curvature ◽  
Riemannian Spaces

The paper contains necessary conditions allowing to reduce matrix tensors of pseudo-Riemannian spaces to special forms called semi-reducible, under assumption that the tensor defining tensor characteristic of semireducibility spaces, is idempotent. The tensor characteristic is reduced to the spaces of constant curvature, Ricci-symmetric spaces and conformally flat pseudo-Riemannian spaces. The obtained results can be applied for construction of examples of spaces belonging to special types of pseudo-Riemannian spaces. The research is carried out locally in tensor shape, without limitations imposed on a sign of a metric.  

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