scholarly journals The Dirichlet problem for Einstein metrics on cohomogeneity one manifolds

2018 ◽  
Vol 54 (1) ◽  
pp. 155-171 ◽  
Author(s):  
Timothy Buttsworth
Keyword(s):  
Dirichlet Problem ◽  
Einstein Metrics ◽  
Cohomogeneity One ◽  
Cohomogeneity One Manifolds

scholarly journals Cohomogeneity-one quasi-Einstein metrics

2019 ◽  
Vol 470 (1) ◽  
pp. 201-217
Author(s):  
Timothy Buttsworth
Keyword(s):  
Einstein Metrics ◽  
Cohomogeneity One

scholarly journals SMOOTHNESS CONDITIONS IN COHOMOGENEITY ONE MANIFOLDS

2020 ◽  
Author(s):  
L. VERDIANI ◽  
W. ZILLER
Keyword(s):  
Efficient Method ◽  
Regular Part ◽  
Cohomogeneity One ◽  
Singular Orbit ◽  
Cohomogeneity One Manifolds

Abstract We present an efficient method for determining the conditions that a metric on a cohomogeneity one manifold, defined in terms of functions on the regular part, needs to satisfy in order to extend smoothly to the singular orbit.

scholarly journals Complete Ricci Solitons via Estimates on the Soliton Potential

2020 ◽  
Author(s):  
Matthias Wink
Keyword(s):  
Large Class ◽  
Ricci Solitons ◽  
Growth Estimate ◽  
Cohomogeneity One ◽  
Cohomogeneity One Manifolds

Abstract In this paper, a growth estimate on the soliton potential is shown for a large class of cohomogeneity one manifolds. This is used to construct continuous families of complete steady and expanding Ricci solitons in the setups of Lü–Page–Pope [ 24] and Dancer–Wang [ 17]. It also provides a different approach to the two summands system [ 30] that applies to all known geometric examples.

Cohomogeneity one manifolds and hypersurfaces of the euclidean space

1995 ◽  
Vol 13 (2) ◽  
pp. 169-184 ◽  
Author(s):  
Fabio Podest� ◽  
Andrea Spiro
Keyword(s):  
Euclidean Space ◽  
Cohomogeneity One ◽  
Cohomogeneity One Manifolds

scholarly journals Seven dimensional cohomogeneity one manifolds with nonnegative curvature

2018 ◽  
Vol 371 (1-2) ◽  
pp. 655-662
Author(s):  
Luigi Verdiani ◽  
Wolfgang Ziller
Keyword(s):  
Nonnegative Curvature ◽  
Cohomogeneity One ◽  
Cohomogeneity One Manifolds

Affine compact almost-homogeneous manifolds of cohomogeneity one

2009 ◽  
Vol 7 (1) ◽  
Author(s):  
Daniel Guan
Keyword(s):  
Einstein Metrics ◽  
Compact Manifolds ◽  
Complex Manifolds ◽  
Homogeneous Manifolds ◽  
Einstein Manifolds ◽  
Extremal Metrics ◽  
Cohomogeneity One ◽  
Fano Manifolds ◽  
Kähler Einstein Metrics

AbstractThis paper is one in a series generalizing our results in [12, 14, 15, 20] on the existence of extremal metrics to the general almost-homogeneous manifolds of cohomogeneity one. In this paper, we consider the affine cases with hypersurface ends. In particular, we study the existence of Kähler-Einstein metrics on these manifolds and obtain new Kähler-Einstein manifolds as well as Fano manifolds without Kähler-Einstein metrics. As a consequence of our study, we also give a solution to the problem posted by Ahiezer on the nonhomogeneity of compact almost-homogeneous manifolds of cohomogeneity one; this clarifies the classification of these manifolds as complex manifolds. We also consider Fano properties of the affine compact manifolds.

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