scholarly journals Moduli spaces of critical Riemannian metrics with Ln2 norm curvature bounds

2011 ◽  
Vol 226 (2) ◽  
pp. 1307-1330 ◽  
Author(s):  
Xiuxiong Chen ◽  
Brian Weber
Keyword(s):  
Moduli Spaces ◽  
Riemannian Metrics ◽  
Curvature Bounds

scholarly journals Smoothing Riemannian metrics with Ricci curvature bounds

1996 ◽  
Vol 90 (1) ◽  
pp. 49-61 ◽  
Author(s):  
Xianzhe Dai ◽  
Guofang Wei ◽  
Rugang Ye
Keyword(s):  
Ricci Curvature ◽  
Riemannian Metrics ◽  
Curvature Bounds

Spaces and moduli spaces of Riemannian metrics

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

scholarly journals Moduli Spaces of Metrics of Positive Scalar Curvature on Topological Spherical Space Forms

2020 ◽  
Vol 63 (4) ◽  
pp. 901-908
Author(s):  
Philipp Reiser
Keyword(s):  
Scalar Curvature ◽  
Moduli Spaces ◽  
Riemannian Metrics ◽  
Universal Cover ◽  
Positive Scalar Curvature ◽  
Spherical Space ◽  
Space Forms ◽  
Positive Scalar ◽  
Space Of Riemannian Metrics ◽  
Simply Connected

AbstractLet $M$ be a topological spherical space form, i.e., a smooth manifold whose universal cover is a homotopy sphere. We determine the number of path components of the space and moduli space of Riemannian metrics with positive scalar curvature on $M$ if the dimension of $M$ is at least 5 and $M$ is not simply-connected.

Mini-Workshop: Spaces and Moduli Spaces of Riemannian Metrics

2018 ◽  
Vol 14 (1) ◽  
pp. 133-166
Author(s):  
F. Thomas Farrell ◽  
Wilderich Tuschmann
Keyword(s):  
Moduli Spaces ◽  
Riemannian Metrics

scholarly journals An index theorem for end-periodic operators

2015 ◽  
Vol 152 (2) ◽  
pp. 399-444 ◽  
Author(s):  
Tomasz Mrowka ◽  
Daniel Ruberman ◽  
Nikolai Saveliev
Keyword(s):  
Scalar Curvature ◽  
Moduli Spaces ◽  
Differential Operators ◽  
Riemannian Metrics ◽  
Index Theorem ◽  
Positive Scalar Curvature ◽  
Fredholm Theory ◽  
Eta Invariant ◽  
First Order ◽  
Periodic Operators

We extend the Atiyah, Patodi, and Singer index theorem for first-order differential operators from the context of manifolds with cylindrical ends to manifolds with periodic ends. This theorem provides a natural complement to Taubes’ Fredholm theory for general end-periodic operators. Our index theorem is expressed in terms of a new periodic eta-invariant that equals the Atiyah–Patodi–Singer eta-invariant in the cylindrical setting. We apply this periodic eta-invariant to the study of moduli spaces of Riemannian metrics of positive scalar 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.

Moduli Spaces of Riemannian Metrics

2015 ◽  
Author(s):  
Wilderich Tuschmann ◽  
David J. Wraith
Keyword(s):  
Moduli Spaces ◽  
Riemannian Metrics

scholarly journals Moduli spaces for jets of Riemannian metrics at a point

2010 ◽  
Vol 28 (6) ◽  
pp. 672-688 ◽  
Author(s):  
A. Gordillo ◽  
J. Navarro ◽  
J.B. Sancho
Keyword(s):  
Moduli Spaces ◽  
Riemannian Metrics
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