Moduli spaces of Riemannian metrics with negative sectional curvature

2015 ◽  
pp. 89-92
Author(s):  
Wilderich Tuschmann ◽  
David J. Wraith
Keyword(s):  
Sectional Curvature ◽  
Moduli Spaces ◽  
Riemannian Metrics ◽  
Negative Sectional Curvature

scholarly journals On the topology of moduli spaces of non-negatively curved Riemannian metrics

2021 ◽  
Author(s):  
Wilderich Tuschmann ◽  
Michael Wiemeler
Keyword(s):  
Sectional Curvature ◽  
Moduli Spaces ◽  
Riemannian Metrics ◽  
Rational Homotopy ◽  
Analogous Statement ◽  
Open Manifolds ◽  
Negatively Curved ◽  
Space Of Riemannian Metrics ◽  
Negative Sectional Curvature ◽  
Infinite Sequences

AbstractWe study spaces and moduli spaces of Riemannian metrics with non-negative Ricci or non-negative sectional curvature on closed and open manifolds. We construct, in particular, the first classes of manifolds for which these moduli spaces have non-trivial rational homotopy, homology and cohomology groups. We also show that in every dimension at least seven (respectively, at least eight) there exist infinite sequences of closed (respectively, open) manifolds of pairwise distinct homotopy type for which the space and moduli space of Riemannian metrics with non-negative sectional curvature has infinitely many path components. A completely analogous statement holds for spaces and moduli spaces of non-negative Ricci curvature metrics.

scholarly journals Small covers, infra-solvmanifolds and curvature

2015 ◽  
Vol 27 (5) ◽  
Author(s):  
Shintarô Kuroki ◽  
Mikiya Masuda ◽  
Li Yu
Keyword(s):  
Sectional Curvature ◽  
Riemannian Metrics ◽  
Flat Torus ◽  
Combinatorial Structures ◽  
Simple Polytope ◽  
Simple Polytopes ◽  
Small Cover ◽  
Equivalent Conditions

AbstractIt is shown that a small cover (resp. real moment-angle manifold) over a simple polytope is an infra-solvmanifold if and only if it is diffeomorphic to a real Bott manifold (resp. flat torus). Moreover, we obtain several equivalent conditions for a small cover to be homeomorphic to a real Bott manifold. In addition, we study Riemannian metrics on small covers and real moment-angle manifolds with certain conditions on the Ricci or sectional curvature. We will see that these curvature conditions put very strong restrictions on the topology of the corresponding small covers and real moment-angle manifolds and the combinatorial structures of the underlying simple polytopes.

Geometry of Manifolds with Non-negative Sectional Curvature

2014 ◽  
Author(s):  
Owen Dearricott ◽  
Fernando Galaz-García ◽  
Lee Kennard ◽  
Catherine Searle ◽  
Gregor Weingart ◽  
...  
Keyword(s):  
Sectional Curvature ◽  
Negative Sectional Curvature

scholarly journals Non-Negative Curvature, Elliptic Genus and Unbounded Pontryagin Numbers

2018 ◽  
Vol 61 (2) ◽  
pp. 449-456
Author(s):  
Martin Herrmann ◽  
Nicolas Weisskopf
Keyword(s):  
Sectional Curvature ◽  
Negative Curvature ◽  
Elliptic Genus ◽  
Negatively Curved ◽  
Spin Manifolds ◽  
Simply Connected ◽  
Negative Sectional Curvature

AbstractWe discuss the cobordism type of spin manifolds with non-negative sectional curvature. We show that in each dimension 4k⩾ 12, there are infinitely many cobordism types of simply connected and non-negatively curved spin manifolds. Moreover, we raise and analyse a question about possible cobordism obstructions to non-negative curvature.

Spaces and moduli spaces of Riemannian metrics

2016 ◽  
Vol 11 (5) ◽  
pp. 1335-1343 ◽  
Author(s):  
Wilderich Tuschmann
Keyword(s):  
Moduli Spaces ◽  
Riemannian Metrics
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