scholarly journals Conformal invariants of twisted Dirac operators and positive scalar curvature

2013 ◽  
Vol 70 ◽  
pp. 39-47 ◽  
Author(s):  
Moulay Tahar Benameur ◽  
Varghese Mathai
Keyword(s):  
Scalar Curvature ◽  
Dirac Operators ◽  
Positive Scalar Curvature ◽  
Conformal Invariants ◽  
Positive Scalar ◽  
Twisted Dirac Operators

scholarly journals Some aspects of Ricci flow on the 4-sphere

10.53733/152 ◽  
2021 ◽  
Vol 52 ◽  
pp. 381-402
Author(s):  
Sun-Yung Alice Chang ◽  
Eric Chen
Keyword(s):  
Scalar Curvature ◽  
Curvature Tensor ◽  
Ricci Flow ◽  
Weyl Tensor ◽  
Riemannian Metrics ◽  
Positive Scalar Curvature ◽  
Conformal Invariants ◽  
Positive Scalar ◽  
Gap Theorem ◽  
Normalized Ricci Flow

In this paper, on 4-spheres equipped with Riemannian metrics we study some integral conformal invariants, the sign and size of which under Ricci flow characterize the standard 4-sphere. We obtain a conformal gap theorem, and for Yamabe metrics of positive scalar curvature with L^2 norm of the Weyl tensor of the metric suitably small, we establish the monotonic decay of the L^p norm for certain p>2 of the reduced curvature tensor along the normalized Ricci flow, with the metric converging exponentially to the standard 4-sphere.

scholarly journals L2-RHO FORM FOR NORMAL COVERINGS OF FIBER BUNDLES

2011 ◽  
Vol 22 (08) ◽  
pp. 1139-1161
Author(s):  
SARA AZZALI
Keyword(s):  
Scalar Curvature ◽  
Large Time ◽  
Dirac Operators ◽  
Positive Scalar Curvature ◽  
Fiber Bundles ◽  
Heat Operator ◽  
Positive Scalar ◽  
Spin Manifolds ◽  
Spectral Projections

We define the secondary invariants L2-eta and -rho forms for families of generalized Dirac operators on normal coverings of fiber bundles. On the covering family we assume transversally smooth spectral projections and Novikov–Shubin invariants bigger than 3( dim B + 1) to treat the large time asymptotic for the heat operator. In the case of a bundle of spin manifolds, we study the L2-rho class in relation to the space [Formula: see text] of positive scalar curvature vertical metrics.

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

scholarly journals Complete hypersurfaces in cylinders

1989 ◽  
Vol 46 (2) ◽  
pp. 313-318
Author(s):  
Thomas Hasanis
Keyword(s):  
Euclidean Space ◽  
Scalar Curvature ◽  
Sectional Curvature ◽  
Positive Scalar Curvature ◽  
Positive Scalar ◽  
Coordinate Functions ◽  
Bounded Below ◽  
Complete Hypersurfaces

AbstractWe consider the extent of certain complete hypersurfaces of Euclidean space. We prove that every complete hypersurface in En+1 with sectional curvature bounded below and non-positive scalar curvature has at least (n − 1) unbounded coordinate functions.

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