Kähler-Einstein metrics with non-positive scalar curvature

2000 ◽  
pp. 43-56
Author(s):  
Gang Tian
Keyword(s):  
Scalar Curvature ◽  
Einstein Metrics ◽  
Positive Scalar Curvature ◽  
Positive Scalar ◽  
Kähler Einstein Metrics

scholarly journals Positivity in Kähler–Einstein theory

2015 ◽  
Vol 159 (2) ◽  
pp. 321-338 ◽  
Author(s):  
GABRIELE DI CERBO ◽  
LUCA F. DI CERBO
Keyword(s):  
Scalar Curvature ◽  
Einstein Metrics ◽  
Cone Angle ◽  
Positive Scalar Curvature ◽  
Einstein Theory ◽  
Uniform Bounds ◽  
Projective Varieties ◽  
Edge Type ◽  
Negatively Curved ◽  
Kähler Einstein Metrics

AbstractTian initiated the study of incomplete Kähler–Einstein metrics on quasi–projective varieties with cone-edge type singularities along a divisor, described by the cone-angle 2π(1-α) for α∈ (0, 1). In this paper we study how the existence of such Kähler–Einstein metrics depends on α. We show that in the negative scalar curvature case, if such Kähler–Einstein metrics exist for all small cone-angles then they exist for every α∈((n+1)/(n+2), 1), wherenis the dimension. We also give a characterisation of the pairs that admit negatively curved cone-edge Kähler–Einstein metrics with cone angle close to 2π. Again if these metrics exist for all cone-angles close to 2π, then they exist in a uniform interval of angles depending on the dimension only. Finally, we show how in the positive scalar curvature case the existence of such uniform bounds is obstructed.

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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