Slab theorem and halfspace theorem for constant mean curvature surfaces in $\mathbb H^2\times\mathbb R$ [PDF]
Revista matemática iberoamericana, 2021 We prove that a properly embedded annular end of a surface in H 2 × R with constant mean curvature 0 < H ≤ 12 can not be contained in any horizontal slab.
L. Hauswirth +2 more
semanticscholar +1 more source
Moduli Spaces of Affine Homogeneous Spaces [PDF]
Bulletin of the Belgian Mathematical Society Simon Stevin, 2017 Apart from global topological problems an affine homogeneous space is locally described by its curvature, its torsion and a slightly less tangible object called its connection in a given base point.
G. Weingart
semanticscholar +1 more source
Covering maps and ideal embeddings of compact homogeneous spaces [PDF]
, 2017 The notion of ideal embeddings was introduced in [B.-Y. Chen, Strings of Riemannian invariants, inequalities, ideal immersions and their applications. The Third Pacific Rim Geometry Conference (Seoul, 1996), 7–60, Int.
Bang‐Yen Chen
semanticscholar +1 more source
Complex product structures on 6-dimensional nilpotent Lie algebras [PDF]
, 2006 We study complex product structures on nilpotent Lie algebras, establishing some of their main properties, and then we restrict ourselves to 6 dimensions, obtaining the classification of 6-dimensional nilpotent Lie algebras admitting such structures.
A. Andrada
semanticscholar +1 more source
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
core +2 more sources
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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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
core +1 more source
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
core +3 more sources
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
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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