scholarly journals Cauchy Kernels for some Conformally Flat Manifolds

2004 ◽  
pp. 149-160 ◽  
Author(s):  
John Ryan
Keyword(s):  
Conformally Flat ◽  
Conformally Flat Manifolds ◽  
Flat Manifolds

scholarly journals The duality of conformally flat manifolds

2011 ◽  
Vol 42 (1) ◽  
pp. 131-152 ◽  
Author(s):  
Huili Liu ◽  
Masaaki Umehara ◽  
Kotaro Yamada
Keyword(s):  
Conformally Flat ◽  
Conformally Flat Manifolds ◽  
Flat Manifolds

scholarly journals Twistor spinors on conformally flat manifolds

1997 ◽  
Vol 41 (3) ◽  
pp. 495-503 ◽  
Author(s):  
Wolfgang Kühnel ◽  
Hans–Bert Rademacher
Keyword(s):  
Conformally Flat ◽  
Conformally Flat Manifolds ◽  
Flat Manifolds

scholarly journals Prescribed diagonal Ricci tensor in locally conformally flat manifolds

2015 ◽  
Vol 421 (1) ◽  
pp. 893-904 ◽  
Author(s):  
Romildo Pina ◽  
Levi Adriano ◽  
Mauricio Pieterzack
Keyword(s):  
Ricci Tensor ◽  
Conformally Flat ◽  
Conformally Flat Manifolds ◽  
Locally Conformally Flat ◽  
Flat Manifolds

scholarly journals Prescribed Schouten Tensor in Locally Conformally Flat Manifolds

2019 ◽  
Vol 74 (4) ◽  
Author(s):  
Marcos Tulio Carvalho ◽  
Mauricio Pieterzack ◽  
Romildo Pina
Keyword(s):  
Sufficient Conditions ◽  
Conformally Flat ◽  
Symmetric Tensors ◽  
Conformally Flat Manifolds ◽  
Dimensional Group ◽  
Schouten Tensor ◽  
Locally Conformally Flat ◽  
Flat Manifolds ◽  
Necessary And Sufficient ◽  
Complete Metrics

Abstract We consider the pseudo-Euclidean space $$({\mathbb {R}}^n,g)$$(Rn,g), with $$n \ge 3$$n≥3 and $$g_{ij} = \delta _{ij} \varepsilon _{i}$$gij=δijεi, where $$\varepsilon _{i} = \pm 1$$εi=±1, with at least one positive $$\varepsilon _{i}$$εi and non-diagonal symmetric tensors $$T = \sum \nolimits _{i,j}f_{ij}(x) dx_i \otimes dx_{j} $$T=∑i,jfij(x)dxi⊗dxj. Assuming that the solutions are invariant by the action of a translation $$(n-1)$$(n-1)- dimensional group, we find the necessary and sufficient conditions for the existence of a metric $$\bar{g}$$g¯ conformal to g, such that the Schouten tensor $$\bar{g}$$g¯, is equal to T. From the obtained results, we show that for certain functions h, defined in $$\mathbb {R}^{n}$$Rn, there exist complete metrics $$\bar{g}$$g¯, conformal to the Euclidean metric g, whose curvature $$\sigma _{2}(\bar{g}) = h$$σ2(g¯)=h.

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