scholarly journals Complete conformal metrics with zero scalar curvature

1992 ◽  
Vol 115 (1) ◽  
pp. 69-69 ◽  
Author(s):  
Xiaoyun Ma ◽  
Robert C. McOwen
Keyword(s):  
Scalar Curvature ◽  
Conformal Metrics ◽  
Zero Scalar Curvature

Topological tools for the prescribed scalar curvature problem on S n

2014 ◽  
Vol 12 (12) ◽  
Author(s):  
Dina Abuzaid ◽  
Randa Ben Mahmoud ◽  
Hichem Chtioui ◽  
Afef Rigane
Keyword(s):  
Scalar Curvature ◽  
Conformal Metrics ◽  
Standard Sphere ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Hopf Formula ◽  
Curvature Problem ◽  
Formula Type

AbstractIn this paper, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere S n, n ≥ 3. We give new existence and multiplicity results based on a new Euler-Hopf formula type. Our argument also has the advantage of extending well known results due to Y. Li [16].

Two-ended hypersurfaces with zero scalar curvature

1999 ◽  
Vol 48 (3) ◽  
pp. 0-0 ◽  
Author(s):  
Jorge Hounie ◽  
Maria Luiza Leite
Keyword(s):  
Scalar Curvature ◽  
Zero Scalar Curvature

scholarly journals Scalar curvatures of conformal metrics on Sn

1995 ◽  
Vol 140 ◽  
pp. 151-166
Author(s):  
Shigeo Kawai
Keyword(s):  
Scalar Curvature ◽  
Unit Sphere ◽  
Gaussian Curvature ◽  
Smooth Function ◽  
Conformal Metrics ◽  
Conformal Metric ◽  
Canonical Metric ◽  
Dimensional Unit ◽  
Dimension 2

In this paper we consider the following problem: Given a smooth function K on the n-dimensional unit sphere Sn(n ≥ 3) with its canonical metric g0, is it possible to find a pointwise conformal metric which has K as its scalar curvature? This problem was presented by J. L. Kazdan and F. W. Warner. The associated problem for Gaussian curvature in dimension 2 had been presented by L. Nirenberg several years before.

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