scholarly journals Positive Ricci curvature on simply-connected manifolds with cohomogeneity-two torus actions

2020 ◽  
Vol 148 (7) ◽  
pp. 3087-3097
Author(s):  
Diego Corro ◽  
Fernando Galaz-García
Keyword(s):  
Ricci Curvature ◽  
Positive Ricci Curvature ◽  
Torus Actions ◽  
Simply Connected Manifolds ◽  
Simply Connected

scholarly journals A note on complete hypersurfaces of non-positive Ricci curvature

1983 ◽  
Vol 28 (3) ◽  
pp. 339-342 ◽  
Author(s):  
G.H. Smith
Keyword(s):  
Euclidean Space ◽  
Recent Result ◽  
Sectional Curvature ◽  
Ricci Curvature ◽  
Riemannian Manifolds ◽  
Positive Constant ◽  
Constant Sectional Curvature ◽  
Positive Ricci Curvature ◽  
Simply Connected ◽  
Complete Hypersurfaces

In this note we point out that a recent result of Leung concerning hypersurfaces of a Euclidean space has a simple generalisation to hypersurfaces of complete simply-connected Riemannian manifolds of non-positive constant sectional curvature.

scholarly journals TOPOLOGICAL 4-MANIFOLDS WITH 4-DIMENSIONAL FUNDAMENTAL GROUP

2021 ◽  
pp. 1-8
Author(s):  
DANIEL KASPROWSKI ◽  
MARKUS LAND
Keyword(s):  
Fundamental Group ◽  
Homotopy Equivalent ◽  
Poincaré Duality ◽  
Poincare Duality ◽  
Canonical Map ◽  
Duality Space ◽  
Simply Connected Manifolds ◽  
Simply Connected ◽  
Poincaré Duality Space

Abstract Let $\pi$ be a group satisfying the Farrell–Jones conjecture and assume that $B\pi$ is a 4-dimensional Poincaré duality space. We consider topological, closed, connected manifolds with fundamental group $\pi$ whose canonical map to $B\pi$ has degree 1, and show that two such manifolds are s-cobordant if and only if their equivariant intersection forms are isometric and they have the same Kirby–Siebenmann invariant. If $\pi$ is good in the sense of Freedman, it follows that two such manifolds are homeomorphic if and only if they are homotopy equivalent and have the same Kirby–Siebenmann invariant. This shows rigidity in many cases that lie between aspherical 4-manifolds, where rigidity is expected by Borel’s conjecture, and simply connected manifolds where rigidity is a consequence of Freedman’s classification results.

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