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- Title
Conformal Rigidity and Non-rigidity of the Scalar Curvature on Riemannian Manifolds.
- Authors
Byeon, Jaeyoung; Jin, Sangdon
- Abstract
For a compact smooth manifold (M , g 0) with a boundary, we study the conformal rigidity and non-rigidity of the scalar curvature in the conformal class. It is known that the sign of the first eigenvalue for a linearized operator of the scalar curvature by a conformal change determines the rigidity/non-rigidity of the scalar curvature by conformal changes when the scalar curvature R g 0 is positive. In this paper, we show the sign condition of R g 0 is not necessary, and a reversed rigidity of the scalar curvature in the conformal class does not hold if there exists a point x 0 ∈ M with R g 0 (x 0) > 0.
- Publication
Journal of Geometric Analysis, 2021, Vol 31, Issue 10, p9745
- ISSN
1050-6926
- Publication type
Article
- DOI
10.1007/s12220-021-00626-z