scholarly journals Positive scalar curvature and the Dirac operator on complete riemannian manifolds

1983 ◽  
Vol 58 (1) ◽  
pp. 83-196 ◽  
Author(s):  
Mikhael Gromov ◽  
H. Blaine Lawson
Keyword(s):  
Dirac Operator ◽  
Scalar Curvature ◽  
Riemannian Manifolds ◽  
Positive Scalar Curvature ◽  
Positive Scalar ◽  
Complete Riemannian Manifolds

Sewing Riemannian Manifolds with Positive Scalar Curvature

2017 ◽  
Vol 28 (4) ◽  
pp. 3553-3602 ◽  
Author(s):  
J. Basilio ◽  
J. Dodziuk ◽  
C. Sormani
Keyword(s):  
Scalar Curvature ◽  
Riemannian Manifolds ◽  
Positive Scalar Curvature ◽  
Positive Scalar

scholarly journals Volume and macroscopic scalar curvature

2021 ◽  
Author(s):  
Sabine Braun ◽  
Roman Sauer
Keyword(s):  
Riemannian Manifold ◽  
Scalar Curvature ◽  
Riemannian Manifolds ◽  
Upper Bound ◽  
Betti Numbers ◽  
Universal Cover ◽  
Positive Scalar Curvature ◽  
Simplicial Volume ◽  
Positive Scalar ◽  
Curvature Bound

AbstractWe prove the macroscopic cousins of three conjectures: (1) a conjectural bound of the simplicial volume of a Riemannian manifold in the presence of a lower scalar curvature bound, (2) the conjecture that rationally essential manifolds do not admit metrics of positive scalar curvature, (3) a conjectural bound of $$\ell ^2$$ ℓ 2 -Betti numbers of aspherical Riemannian manifolds in the presence of a lower scalar curvature bound. The macroscopic cousin is the statement one obtains by replacing a lower scalar curvature bound by an upper bound on the volumes of 1-balls in the universal cover.

scholarly journals PARTIAL CLASSIFICATION RESULTS FOR POSITIVE QUATERNION KÄHLER MANIFOLDS

2012 ◽  
Vol 23 (02) ◽  
pp. 1250038
Author(s):  
MANUEL AMANN
Keyword(s):  
Scalar Curvature ◽  
Riemannian Manifolds ◽  
Symmetric Spaces ◽  
Positive Scalar Curvature ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
The Real ◽  
Positive Scalar ◽  
Partial Classification ◽  
Almost All

Positive Quaternion Kähler Manifolds are Riemannian manifolds with holonomy contained in Sp(n)Sp(1) and with positive scalar curvature. Conjecturally, they are symmetric spaces. We prove this conjecture in dimension 20 under additional assumptions and we provide recognition theorems for the real Grassmannian [Formula: see text] in almost all dimensions.

Positive scalar curvature metrics via end-periodic manifolds

2020 ◽  
Vol 5 (3) ◽  
pp. 639-676
Author(s):  
Michael Hallam ◽  
Varghese Mathai
Keyword(s):  
Scalar Curvature ◽  
Positive Scalar Curvature ◽  
Positive Scalar
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