scholarly journals A sphere theorem for Bach-flat manifolds with positive constant scalar curvature

2019 ◽  
Vol 64 ◽  
pp. 80-91
Author(s):  
Yi Fang ◽  
Wei Yuan
Keyword(s):  
Scalar Curvature ◽  
Positive Constant ◽  
Constant Scalar Curvature ◽  
Sphere Theorem ◽  
Bach Flat ◽  
Flat Manifolds

Some remarks on Bach-flat manifolds with positive constant scalar curvature

2019 ◽  
Vol 155 (2) ◽  
pp. 187-196 ◽  
Author(s):  
Hai-Ping Fu ◽  
Gao-Bo Xu ◽  
Yong-Qian Tao
Keyword(s):  
Scalar Curvature ◽  
Positive Constant ◽  
Constant Scalar Curvature ◽  
Bach Flat ◽  
Flat Manifolds

Partially regular and cscK metrics

2020 ◽  
Vol 31 (10) ◽  
pp. 2050079
Author(s):  
Andrea Loi ◽  
Fabio Zuddas
Keyword(s):  
Scalar Curvature ◽  
Complex Manifold ◽  
Positive Constant ◽  
Bergman Kernel ◽  
Constant Scalar Curvature ◽  
Kähler Metric ◽  
Kähler Form ◽  
Kahler Metric

A Kähler metric [Formula: see text] with integral Kähler form is said to be partially regular if the partial Bergman kernel associated to [Formula: see text] is a positive constant for all integer [Formula: see text] sufficiently large. The aim of this paper is to prove that for all [Formula: see text] there exists an [Formula: see text]-dimensional complex manifold equipped with strictly partially regular and cscK metric [Formula: see text]. Further, for [Formula: see text], the (constant) scalar curvature of [Formula: see text] can be chosen to be zero, positive or negative.

CONFORMAL TRANSFORMATIONS OF COMPACT SELF-DUAL MANIFOLDS

1994 ◽  
Vol 05 (01) ◽  
pp. 125-140 ◽  
Author(s):  
Y. S. POON
Keyword(s):  
Scalar Curvature ◽  
Symmetry Group ◽  
Positive Constant ◽  
Three Dimensional ◽  
Constant Scalar Curvature ◽  
Topological Classification ◽  
Conformal Transformations ◽  
Conformal Class ◽  
Zero Scalar Curvature

We prove that when the dimension of the group of conformal transformations of a compact self-dual manifold is at least three, the conformal class contains either a metric with positive constant scalar curvature or a metric with zero scalar curvature. This result is combined with a topological classification of 4-manifolds to provide a complete geometrical classification of the compact self-dual manifolds whose symmetry group is at least three-dimensional.

Yamabe solitons on 3-dimensional contact metric manifolds with Qφ = φQ

2019 ◽  
Vol 16 (03) ◽  
pp. 1950039 ◽  
Author(s):  
V. Venkatesha ◽  
Devaraja Mallesha Naik
Keyword(s):  
Vector Field ◽  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
Sasakian Manifold ◽  
Contact Metric Manifold ◽  
Reeb Vector Field ◽  
3 Dimensional ◽  
Flow Vector ◽  
Contact Metric Manifolds ◽  
Yamabe Soliton

If [Formula: see text] is a 3-dimensional contact metric manifold such that [Formula: see text] which admits a Yamabe soliton [Formula: see text] with the flow vector field [Formula: see text] pointwise collinear with the Reeb vector field [Formula: see text], then we show that the scalar curvature is constant and the manifold is Sasakian. Moreover, we prove that if [Formula: see text] is endowed with a Yamabe soliton [Formula: see text], then either [Formula: see text] is flat or it has constant scalar curvature and the flow vector field [Formula: see text] is Killing. Furthermore, we show that if [Formula: see text] is non-flat, then either [Formula: see text] is a Sasakian manifold of constant curvature [Formula: see text] or [Formula: see text] is an infinitesimal automorphism of the contact metric structure on [Formula: see text].

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