Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
134 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

$η$-Einstein Sasakian Lie algebras (2504.16033v1)

Published 22 Apr 2025 in math.DG

Abstract: We study $\eta$-Einstein Sasakian structures on Lie algebras, that is, Sasakian structures whose associated Ricci tensor satisfies an Einstein-like condition. We divide into the cases in which the Lie algebra's centre is non-trivial (and necessarily one-dimensional) and those where it is zero. In the former case we show that any Sasakian structure on a unimodular Lie algebra is $\eta$-Einstein. As for centreless Sasakian Lie algebras, we devise a complete characterisation under certain dimensional assumptions regarding the action of the Reeb vector. Using this result, together with the theory of normal $j$-algebras and modifications of Hermitian Lie algebras, we construct new examples of $\eta$-Einstein Sasakian Lie algebras and solvmanifolds, and provide effective restrictions for their existence.

Summary

We haven't generated a summary for this paper yet.