Short geodesics for Ad invariant metrics in locally exponential Lie groups

2019 ◽  
pp. 153-160
Author(s):  
Gabriel Larotonda
Keyword(s):  
Lie Groups ◽  
Invariant Metrics ◽  
Exponential Lie Groups

scholarly journals Construction of canonical coordinates for exponential Lie groups

2009 ◽  
Vol 361 (12) ◽  
pp. 6283-6348 ◽  
Author(s):  
Didier Arnal ◽  
Bradley Currey ◽  
Bechir Dali
Keyword(s):  
Lie Groups ◽  
Canonical Coordinates ◽  
Exponential Lie Groups

scholarly journals The Ricci pinching functional on solvmanifolds

2019 ◽  
Author(s):  
Jorge Lauret ◽  
Cynthia E Will
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Invariant Metrics ◽  
Solvable Lie Groups ◽  
Left Invariant Metrics ◽  
Solvable Lie Group

Abstract We study the natural functional $F=\frac {\operatorname {scal}^2}{|\operatorname {Ric}|^2}$ on the space of all non-flat left-invariant metrics on all solvable Lie groups of a given dimension $n$. As an application of properties of the beta operator, we obtain that solvsolitons are the only global maxima of $F$ restricted to the set of all left-invariant metrics on a given unimodular solvable Lie group, and beyond the unimodular case, we obtain the same result for almost-abelian Lie groups. Many other aspects of the behavior of $F$ are clarified.

scholarly journals Invariant Metrics with Nonnegative Curvature on Compact Lie Groups

2007 ◽  
Vol 50 (1) ◽  
pp. 24-34 ◽  
Author(s):  
Nathan Brown ◽  
Rachel Finck ◽  
Matthew Spencer ◽  
Kristopher Tapp ◽  
Zhongtao Wu
Keyword(s):  
Sectional Curvature ◽  
Lie Groups ◽  
Nonnegative Curvature ◽  
Invariant Metrics ◽  
Compact Lie Groups ◽  
Nonnegative Sectional Curvature ◽  
Left Invariant Metrics

AbstractWe classify the left-invariant metrics with nonnegative sectional curvature on SO(3) and U(2).

scholarly journals Vacuum quantum effects on Lie groups with bi-invariant metrics

2019 ◽  
Vol 16 (08) ◽  
pp. 1950122
Author(s):  
A. I. Breev ◽  
A. V. Shapovalov
Keyword(s):  
Scalar Field ◽  
Lie Groups ◽  
Separation Of Variables ◽  
Three Dimensional ◽  
Particle Creation ◽  
Vacuum Expectation ◽  
Rotation Group ◽  
Momentum Tensor ◽  
Invariant Metrics ◽  
Field Equations

We consider the effects of vacuum polarization and particle creation of a scalar field on Lie groups with a non-stationary bi-invariant metric of the Robertson–Walker type. The vacuum expectation values of the energy momentum tensor for a scalar field determined by the group representation are found using the noncommutative integration method for the field equations instead of separation of variables. The results obtained are illustrated by the example of the three-dimensional rotation group.

scholarly journals Weakly Exponential Lie Groups

1996 ◽  
Vol 179 (2) ◽  
pp. 331-361 ◽  
Author(s):  
Karl-Hermann Neeb
Keyword(s):  
Lie Groups ◽  
Exponential Lie Groups

scholarly journals Spectral isolation of bi-invariant metrics on compact Lie groups

2010 ◽  
Vol 60 (5) ◽  
pp. 1617-1628 ◽  
Author(s):  
Carolyn S. Gordon ◽  
Dorothee Schueth ◽  
Craig J. Sutton
Keyword(s):  
Lie Groups ◽  
Invariant Metrics ◽  
Compact Lie Groups
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