Invariant Metrics

1989 ◽  
pp. 63-111 ◽  
Author(s):  
E. A. Poletskiľ ◽  
B. V. Shabat
Keyword(s):  
Invariant Metrics

scholarly journals Estimates for invariant metrics on $\mathbb C$-convex domains

2011 ◽  
Vol 363 (12) ◽  
pp. 6245-6256 ◽  
Author(s):  
Nikolai Nikolov ◽  
Peter Pflug ◽  
Włodzimierz Zwonek
Keyword(s):  
Invariant Metrics ◽  
Convex Domains

Geometric structures on manifolds and holonomy-invariant metrics

1997 ◽  
Vol 9 (9) ◽  
Author(s):  
Suhyoung Choi ◽  
Hyunkoo Lee
Keyword(s):  
Invariant Metrics ◽  
Geometric Structures

scholarly journals Scale Invariant Metrics of Volumetric Datasets

2015 ◽  
Vol 8 (1) ◽  
pp. 403-425 ◽  
Author(s):  
Dan Raviv ◽  
Ramesh Raskar
Keyword(s):  
Invariant Metrics ◽  
Scale Invariant

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, An Important Tool in Several Complex Variables

2020 ◽  
Vol 30 (2) ◽  
pp. 1173-1173
Author(s):  
Marek Jarnicki ◽  
Steven G. Krantz ◽  
Peter Pflug
Keyword(s):  
Complex Variables ◽  
Several Complex Variables ◽  
Invariant Metrics

Naturally Reductive Homogeneous Riemannian Manifolds

1985 ◽  
Vol 37 (3) ◽  
pp. 467-487 ◽  
Author(s):  
Carolyn S. Gordon
Keyword(s):  
Homogeneous Space ◽  
Lie Group ◽  
Riemannian Manifolds ◽  
Homogeneous Spaces ◽  
Invariant Metrics ◽  
List Type ◽  
Left Invariant Metrics ◽  
Homogeneous Riemannian Manifolds ◽  
Transitive Subgroup ◽  
Naturally Reductive

The simple algebraic and geometric properties of naturally reductive metrics make them useful as examples in the study of homogeneous Riemannian manifolds. (See for example [2], [3], [15]). The existence and abundance of naturally reductive left-invariant metrics on a Lie group G or homogeneous space G/L reflect the structure of G itself. Such metrics abound on compact groups, exist but are more restricted on noncompact semisimple groups, and are relatively rare on solvable groups. The goals of this paper are(i) to study all naturally reductive homogeneous spaces of G when G is either semisimple of noncompact type or nilpotent and(ii) to give necessary conditions on a Riemannian homogeneous space of an arbitrary Lie group G in order that the metric be naturally reductive with respect to some transitive subgroup of G.

scholarly journals Families of(1,2)-symplectic metrics on full flag manifolds

2002 ◽  
Vol 29 (11) ◽  
pp. 651-664 ◽  
Author(s):  
Marlio Paredes
Keyword(s):  
Flag Manifolds ◽  
Invariant Metrics ◽  
Complex Structures ◽  
Symplectic Invariant ◽  
Almost Complex Structures ◽  
Almost Complex ◽  
Complex Flag ◽  
Complex Flag Manifolds

We obtain new families of(1,2)-symplectic invariant metrics on the full complex flag manifoldsF(n). Forn≥5, we characterizen−3differentn-dimensional families of(1,2)-symplectic invariant metrics onF(n). Each of these families corresponds to a different class of nonintegrable invariant almost complex structures onF(n).

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