Results 1 to 10 of about 738 (35)
Complex Manifolds, 2022 We give a complete classification of left invariant para-Kähler structures on four-dimensional simply connected Lie groups up to an automorphism. As an application we discuss some curvatures properties of the canonical connection associated to these ...
Mansouri M. W., Oufkou A.
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On Degenerate 3-(α, δ)-Sasakian Manifolds
Complex Manifolds, 2022 We propose a new method to construct degenerate 3-(α, δ)-Sasakian manifolds as fiber products of Boothby-Wang bundles over hyperkähler manifolds. Subsequently, we study homogeneous degenerate 3-(α, δ)-Sasakian manifolds and prove that no non-trivial ...
Goertsches Oliver +2 more
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Locally conformally balanced metrics on almost abelian Lie algebras
Complex Manifolds, 2021 We study locally conformally balanced metrics on almost abelian Lie algebras, namely solvable Lie algebras admitting an abelian ideal of codimension one, providing characterizations in every dimension. Moreover, we classify six-dimensional almost abelian
Paradiso Fabio
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An Integrability Condition for Simple Lie Groups II [PDF]
, 2015 It is shown that a simple Lie group $G$ ($ \neq {\rm SL}_2$) can be locally characterised by an integrability condition on an $\operatorname{Aut}(\mathfrak{g})$ structure on the tangent bundle, where $\operatorname{Aut}(\mathfrak{g})$ is the automorphism
Min-Oo, Maung
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On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group [PDF]
, 2010 In this note we prove that the Heisenberg group with a left-invariant pseudo-Riemannian metric admits a completely integrable totally geodesic distribution of codimension 1.
Batat, Wafaa, Rahmani, Salima
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A remark on the Bismut-Ricci form on 2-step nilmanifolds [PDF]
, 2017 In this note we observe that on a 2-step nilpotent Lie group equipped with a left-invariant SKT structure the (1,1)-part of the Bismut-Ricci form is seminegative definite.
Pujia, Mattia, Vezzoni, Luigi
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On the smallest Laplace eigenvalue for naturally reductive metrics on compact simple Lie groups [PDF]
, 2019 Eldredge, Gordina and Saloff-Coste recently conjectured that, for a given compact connected Lie group $G$, there is a positive real number $C$ such that $\lambda_1(G,g)\operatorname{diam}(G,g)^2\leq C$ for all left-invariant metrics $g$ on $G$.
Lauret, Emilio Agustin
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Complex structures on the complexification of a real Lie algebra
Complex Manifolds, 2018 Let g = a+b be a Lie algebra with a direct sum decomposition such that a and b are Lie subalgebras. Then, we can construct an integrable complex structure J̃ on h = ℝ(gℂ) from the decomposition, where ℝ(gℂ) is a real Lie algebra obtained from gℂby the ...
Yamada Takumi
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Homogeneous Riemannian Structures on Berger 3-Spheres [PDF]
, 2005 13 pages.-- MSC2000 codes: 53C30, 53C25.The homogeneous Riemannian structures on the 3-dimensional Berger spheres, their corresponding reductive decompositions and the associated groups of isometries are obtained.
Grosshans, Frank D. +2 more
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Ricci-flat and Einstein pseudoriemannian nilmanifolds
Complex Manifolds, 2019 This is partly an expository paper, where the authors’ work on pseudoriemannian Einstein metrics on nilpotent Lie groups is reviewed. A new criterion is given for the existence of a diagonal Einstein metric on a nice nilpotent Lie group.
Conti Diego, Rossi Federico A.
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