scholarly journals ALMOST KAHLER METRICS WITH NON-POSITIVE SCALAR CURVATURE WHICH ARE EUCLIDEAN AWAY FROM A COMPACT SET

2004 ◽  
Vol 41 (5) ◽  
pp. 809-820 ◽  
Author(s):  
Yu-Tae Kang ◽  
Jong-Su Kim
Keyword(s):  
Scalar Curvature ◽  
Positive Scalar Curvature ◽  
Compact Set ◽  
Kähler Metrics ◽  
Kahler Metrics ◽  
Positive Scalar ◽  
Almost Kähler

Callias-type operators in C∗-algebras and positive scalar curvature on noncompact manifolds

2018 ◽  
Vol 12 (04) ◽  
pp. 897-939 ◽  
Author(s):  
Simone Cecchini
Keyword(s):  
Scalar Curvature ◽  
Riemannian Metrics ◽  
Index Theorem ◽  
Complete Riemannian Manifold ◽  
Positive Scalar Curvature ◽  
Type Operator ◽  
Spin Manifold ◽  
Compact Set ◽  
Positive Scalar ◽  
C Algebras

A Dirac-type operator on a complete Riemannian manifold is of Callias-type if its square is a Schrödinger-type operator with a potential uniformly positive outside of a compact set. We develop the theory of Callias-type operators twisted with Hilbert [Formula: see text]-module bundles and prove an index theorem for such operators. As an application, we derive an obstruction to the existence of complete Riemannian metrics of positive scalar curvature on noncompact spin manifolds in terms of closed submanifolds of codimension one. In particular, when [Formula: see text] is a closed spin manifold, we show that if the cylinder [Formula: see text] carries a complete metric of positive scalar curvature, then the (complex) Rosenberg index on [Formula: see text] must vanish.

scholarly journals Scalar Curvature Functions of Almost-Kähler Metrics

2015 ◽  
Vol 26 (4) ◽  
pp. 2711-2728
Author(s):  
Jongsu Kim ◽  
Chanyoung Sung
Keyword(s):  
Scalar Curvature ◽  
Kähler Metrics ◽  
Kahler Metrics ◽  
Almost Kähler

scholarly journals EXTREMAL ALMOST-KÄHLER METRICS

2010 ◽  
Vol 21 (12) ◽  
pp. 1639-1662 ◽  
Author(s):  
MEHDI LEJMI
Keyword(s):  
Vector Field ◽  
Scalar Curvature ◽  
Explicit Formula ◽  
Cohomology Class ◽  
Symplectic Form ◽  
Kähler Metrics ◽  
Kahler Metrics ◽  
Integral Cohomology ◽  
Almost Kähler ◽  
Compact Kähler Manifold

We generalize the notions of the Futaki invariant and extremal vector field of a compact Kähler manifold to the general almost-Kähler case and show the periodicity of the extremal vector field when the symplectic form represents an integral cohomology class modulo torsion. We also give an explicit formula of the Hermitian scalar curvature in Darboux coordinates which allows us to obtain examples of non-integrable extremal almost-Kähler metrics saturating LeBrun's estimates.

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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