Classification of left-invariant Einstein metrics on $$\textrm{SL}(2,\mathbb {R})\times \textrm{SL}(2,\mathbb {R})$$ that are bi-invariant under a one-parameter subgroup

Cortés, Vicente; Jeremias, Ehlert,; Haupt, Alexander S.; Lindemann, David

doi:10.1007/s10455-023-09890-4

Ann Glob Anal Geom

2023

DOI: 10.1007/s10455-023-09890-4

|View full text |Cite

Classification of left-invariant Einstein metrics on $$\textrm{SL}(2,\mathbb {R})\times \textrm{SL}(2,\mathbb {R})$$ that are bi-invariant under a one-parameter subgroup

Vicente Cortés

Ehlert, Jeremias

Alexander S. Haupt

et al.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2023

Publication Types

Select...

Article1

Relationship

Self Cite1

Independent0

Authors

Journals

Cited by 1 publication

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Classification of generalized Einstein metrics on three-dimensional Lie groups

Cortés¹,

David²

2023

Can. J. Math.-J. Can. Math.

Self Cite

View full text Add to dashboard Cite

We develop the theory of left-invariant generalized pseudo-Riemannian metrics on Lie groups. Such a metric accompanied by a choice of left-invariant divergence operator gives rise to a Ricci curvature tensor and we study the corresponding Einstein equation. We compute the Ricci tensor in terms of the tensors (on the sum of the Lie algebra and its dual) encoding the Courant algebroid structure, the generalized metric and the divergence operator. The resulting expression is polynomial and homogeneous of degree two in the coefficients of the Dorfman bracket and the divergence operator with respect to a left-invariant orthonormal basis for the generalized metric. We determine all generalized Einstein metrics on three-dimensional Lie groups.

show abstract

Classification of generalized Einstein metrics on three-dimensional Lie groups

Cortés¹,

David²

2023

Can. J. Math.-J. Can. Math.

Self Cite

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Classification of left-invariant Einstein metrics on $$\textrm{SL}(2,\mathbb {R})\times \textrm{SL}(2,\mathbb {R})$$ that are bi-invariant under a one-parameter subgroup

Cited by 1 publication

References 9 publications

Classification of generalized Einstein metrics on three-dimensional Lie groups

Classification of generalized Einstein metrics on three-dimensional Lie groups

Contact Info

Product

Resources

About