Non-negative sectional curvature moduli spaces on open manifolds

2015 ◽  
pp. 93-98
Author(s):  
Wilderich Tuschmann ◽  
David J. Wraith
Keyword(s):  
Sectional Curvature ◽  
Moduli Spaces ◽  
Open Manifolds ◽  
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.

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.

scholarly journals On para-Kenmotsu manifolds

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 4971-4980 ◽  
Author(s):  
Simeon Zamkovoy
Keyword(s):  
Sectional Curvature ◽  
Ricci Tensor ◽  
Constant Scalar Curvature ◽  
Holomorphic Sectional Curvature ◽  
Kenmotsu Manifold ◽  
3 Dimensional ◽  
Kenmotsu Manifolds ◽  
Locally Conformally Flat ◽  
Parallel Ricci Tensor ◽  
Negative Sectional Curvature

In this paper we study para-Kenmotsu manifolds. We characterize this manifolds by tensor equations and study their properties. We are devoted to a study of ?-Einstein manifolds. We show that a locally conformally flat para-Kenmotsu manifold is a space of constant negative sectional curvature -1 and we prove that if a para-Kenmotsu manifold is a space of constant ?-para-holomorphic sectional curvature H, then it is a space of constant sectional curvature and H = -1. Finally the object of the present paper is to study a 3-dimensional para-Kenmotsu manifold, satisfying certain curvature conditions. Among other, it is proved that any 3-dimensional para-Kenmotsu manifold with ?-parallel Ricci tensor is of constant scalar curvature and any 3-dimensional para-Kenmotsu manifold satisfying cyclic Ricci tensor is a manifold of constant negative sectional curvature -1.

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