Conformally flat manifolds with nonnegative Ricci curvature
Gilles Carron, Marc Herzlich
Abstract
We show that complete conformally flat manifolds of dimension n>2 with nonnegative Ricci curvature enjoy nice rigidity properties: they are either flat, or locally isometric to a product of a sphere and a line, or are globally conformally equivalent to flat space or to a spherical spaceform. This extends previous works by Q.-M. Cheng, M.H. Noronha, B.-L. Chen and X.-P. Zhu, and S. Zhu.
Create a lesson
Related papers
A note on the BRST-BV Formalism Explanation of Deformation Quantization and Algebraic Index Theorem
Lihao Zhao
Biharmonic submanifolds in nonpositive space forms
Yu Fu, Min-chun Hong, Dan Yang
Conjugate radius and parabolicity along the Ricci flow
Chandan Kumar Mondal
Pure Spinor Factorization of Belinski-Zakharov Solitons and Regular Gravitational Instantons
Steffen Aksteiner
Flexibility of Laplace-Beltrami eigenfunctions under metric variation
Andrei Agrachev, Nicola Da Ponte, Antonio Lerario et al.
C1-rigidity of Hp,q-convex cocompact representations of Gromov hyperbolic groups
Nikolay Bogachev