Results 1 to 10 of about 1,668 (62)
Preferred Parameterisations on Homogeneous Curves [PDF]
arXiv, 2003 We show how to specify preferred parameterisations on a homogeneous curve in an arbitrary homogeneous space. We apply these results to limit the natural parameters on distinguished curves in parabolic geometries.Comment: 10 ...
Eastwood, Michael, Slovak, Jan
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Some Non-Compactness Results for Locally Homogeneous Contact Metric Manifolds [PDF]
, 2022 We exhibit some sufficient conditions ensuring the non-compactness of a locally homogeneous, regular, contact metric manifold, under suitable assumptions on the Jacobi operator of the Reeb vector field. Mathematics Subject Classification. 53C25, 53C30.
Lotta, Antonio +1 more
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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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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
doaj +1 more source
Invariant Matsumoto metrics on homogeneous spaces [PDF]
, 2013 In this paper we consider invariant Matsumoto metrics which are induced by invariant Riemannian metrics and invariant vector fields on homogeneous spaces then we give the flag curvature formula of them.
Moghaddam, H. R. Salimi
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Isometry Lie algebras of indefinite homogeneous spaces of finite volume
Proceedings of the London Mathematical Society, Volume 119, Issue 4, Page 1115-1148, October 2019., 2019 Abstract Let g be a real finite‐dimensional Lie algebra equipped with a symmetric bilinear form ⟨·,·⟩. We assume that ⟨·,·⟩ is nil‐invariant. This means that every nilpotent operator in the smallest algebraic Lie subalgebra of endomorphisms containing the adjoint representation of g is an infinitesimal isometry for ⟨·,·⟩.
Oliver Baues +2 more
wiley +1 more source