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.

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