Metrics of Positive Scalar Curvature on Spherical Space Forms

1996 ◽  
Vol 48 (1) ◽  
pp. 64-80 ◽  
Author(s):  
Boris Botvinnik ◽  
Peter B. Gilkey
Keyword(s):  
Scalar Curvature ◽  
Space Form ◽  
Positive Scalar Curvature ◽  
Spherical Space ◽  
Space Forms ◽  
Eta Invariant ◽  
Positive Scalar ◽  
Spherical Space Forms ◽  
Simply Connected ◽  
Spherical Space Form

AbstractWe use the eta invariant to show every non-simply connected spherical space form of dimension m ≥ 5 has a countable family of non bordant metrics of positive scalar curvature.

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.

scholarly journals On Moduli Spaces of Positive Scalar Curvature Metrics on Highly Connected Manifolds

2020 ◽  
Author(s):  
Michael Wiemeler
Keyword(s):  
Fundamental Group ◽  
Scalar Curvature ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Positive Scalar Curvature ◽  
Spin Manifold ◽  
Homotopy Groups ◽  
Positive Scalar ◽  
Simply Connected ◽  
Highly Connected Manifolds

Abstract Let $M$ be a simply connected spin manifold of dimension at least six, which admits a metric of positive scalar curvature. We show that the observer moduli space of positive scalar curvature metrics on $M$ has non-trivial higher homotopy groups. Moreover, denote by $\mathcal{M}_0^+(M)$ the moduli space of positive scalar curvature metrics on $M$ associated to the group of orientation-preserving diffeomorphisms of $M$. We show that if $M$ belongs to a certain class of manifolds that includes $(2n-2)$-connected $(4n-2)$-dimensional manifolds, then the fundamental group of $\mathcal{M}_0^+(M)$ is non-trivial.

A note on a three-dimensional sphere theorem with integral curvature condition

2016 ◽  
Vol 18 (04) ◽  
pp. 1550070 ◽  
Author(s):  
Mijia Lai
Keyword(s):  
Scalar Curvature ◽  
Ricci Curvature ◽  
Space Form ◽  
Three Dimensional ◽  
Dimensional Sphere ◽  
Integral Curvature ◽  
Spherical Space ◽  
Sphere Theorem ◽  
Curvature Condition ◽  
Spherical Space Form

In this paper, we obtain a three-dimensional sphere theorem with integral curvature condition. On a closed three manifold [Formula: see text] with constant positive scalar curvature, if a certain combination of [Formula: see text] norm of the Ricci curvature and [Formula: see text] norm of the scalar curvature is positive, then [Formula: see text] is diffeomorphic to a spherical space form.

scholarly journals Einstein Four-Manifolds With Self-Dual Weyl Curvature of Nonnegative Determinant

2019 ◽  
Author(s):  
Peng Wu
Keyword(s):  
Scalar Curvature ◽  
Positive Scalar Curvature ◽  
The Self ◽  
Weyl Curvature ◽  
Positive Scalar ◽  
Four Manifolds ◽  
Simply Connected

Abstract We prove that simply connected Einstein four-manifolds of positive scalar curvature are conformally Kähler if and only if the determinant of the self-dual Weyl curvature is positive.

The Eta Invariant and Equivariant SpinC Bordism for Spherical Space form Groups

1988 ◽  
Vol 40 (2) ◽  
pp. 392-428 ◽  
Author(s):  
Peter B. Gilkey
Keyword(s):  
Space Form ◽  
Spherical Space ◽  
Eta Invariant ◽  
Eta Invariants ◽  
Whitney Numbers ◽  
Free Representation ◽  
A Finite Group ◽  
Prime 2 ◽  
Coefficient Ring ◽  
Spherical Space Form

A finite group G is a spherical space form group if it admits a fixed point free representation τ:G → U(k) for some k; for the remainder of this paper, we assume G is such a group. The eta invariant of Atiyah et al [2] defines Q/Z valued invariants of equivariant bordism. In [6], we showed the eta invariant completely detects the reduced equivariant unitary bordism groups and completely detects all but the 2-primary part of the reduced equivariant SpinC bordism groups . The coefficient ring is without torsion; all the torsion in is of order 2. The prime 2 plays a distinguished role in the discussion of equivariant SpinC bordism and is quite different from at the prime 2. Let ker*(η, G) denote the kernel of all eta invariants and let ker*(SW, G) denote the kernel of the Z2-equivariant Stiefel-Whitney numbers (see Section 1 for details). Then:THEOREM 0.1. Let. If M = ker*(η, G) ∩ ker*(SW, G), M = 0.

Sign in / Sign up

Export Citation Format

Share Document