Compact six-dimensional K�hler spin manifolds of positive scalar curvature with the smallest possible first eigenvalue of the Dirac operator

1988 ◽  
Vol 282 (1) ◽  
pp. 157-176 ◽  
Author(s):  
K. D. Kirchberg
Keyword(s):  
Dirac Operator ◽  
Scalar Curvature ◽  
Positive Scalar Curvature ◽  
First Eigenvalue ◽  
Positive Scalar ◽  
Spin Manifolds

scholarly journals On Gromov’s conjecture for totally non-spin manifolds

2016 ◽  
Vol 08 (04) ◽  
pp. 571-587
Author(s):  
Dmitry Bolotov ◽  
Alexander Dranishnikov
Keyword(s):  
Fundamental Group ◽  
Scalar Curvature ◽  
Universal Covering ◽  
Positive Scalar Curvature ◽  
Fundamental Groups ◽  
Closed Formula ◽  
Duality Group ◽  
Positive Scalar ◽  
Spin Manifolds ◽  
Stability Conjecture

Gromov’s conjecture states that for a closed [Formula: see text]-manifold [Formula: see text] with positive scalar curvature, the macroscopic dimension of its universal covering [Formula: see text] satisfies the inequality [Formula: see text] [9]. We prove that for totally non-spin [Formula: see text]-manifolds, the inequality [Formula: see text] implies the inequality [Formula: see text]. This implication together with the main result of [6] allows us to prove Gromov’s conjecture for totally non-spin [Formula: see text]-manifolds whose fundamental group is a virtual duality group with [Formula: see text]. In the case of virtually abelian groups, we reduce Gromov’s conjecture for totally non-spin manifolds to the problem whether [Formula: see text]. This problem can be further reduced to the [Formula: see text]-stability conjecture for manifolds with free abelian fundamental groups.

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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