Transitive riemannian isometry groups with nilpotent radicals

C. Gordon

Displaying similar documents to “Transitive riemannian isometry groups with nilpotent radicals”

On holomorphically separable complex solv-manifolds

Alan T. Huckleberry, E. Oeljeklaus (1986)

Annales de l'institut Fourier

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Let $G$ be a solvable complex Lie group and $H$ a closed complex subgroup of $G$ . If the global holomorphic functions of the complex manifold $X : G / H$ locally separate points on $X$ , then $X$ is a Stein manifold. Moreover there is a subgroup $\hat{H}$ of finite index in $H$ with $π_{1} (G / \hat{H})$ nilpotent. In special situations (e.g. if $H$ is discrete) $H$ normalizes $\hat{H}$ and $H / \hat{H}$ is abelian.

Classification of 2-step nilpotent Lie algebras of dimension 9 with 2-dimensional center

Bin Ren, Lin Sheng Zhu (2017)

Czechoslovak Mathematical Journal

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A Lie algebra $L$ is called 2-step nilpotent if $L$ is not abelian and $[L, L]$ lies in the center of $L$ . 2-step nilpotent Lie algebras are useful in the study of some geometric problems, and their classification has been an important problem in Lie theory. In this paper, we give a classification of 2-step nilpotent Lie algebras of dimension 9 with 2-dimensional center.

Invariants of complex structures on nilmanifolds

Edwin Alejandro Rodríguez Valencia (2015)

Archivum Mathematicum

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Let $(N, J)$ be a simply connected $2 n$ -dimensional nilpotent Lie group endowed with an invariant complex structure. We define a left invariant Riemannian metric on $N$ compatible with $J$ to be minimal, if it minimizes the norm of the invariant part of the Ricci tensor among all compatible metrics with the same scalar curvature. In [7], J. Lauret proved that minimal metrics (if any) are unique up to isometry and scaling. This uniqueness allows us to distinguish two complex structures with Riemannian...

An application of Lie groupoids to a rigidity problem of 2-step nilmanifolds

Hamid-Reza Fanaï, Atefeh Hasan-Zadeh (2019)

Mathematica Bohemica

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We study a problem of isometric compact 2-step nilmanifolds $M / Γ$ using some information on their geodesic flows, where $M$ is a simply connected 2-step nilpotent Lie group with a left invariant metric and $Γ$ is a cocompact discrete subgroup of isometries of $M$ . Among various works concerning this problem, we consider the algebraic aspect of it. In fact, isometry groups of simply connected Riemannian manifolds can be characterized in a purely algebraic way, namely by normalizers. So, suitable...

Finite groups in which every self-centralizing subgroup is nilpotent or subnormal or a TI-subgroup

Jiangtao Shi, Na Li (2021)

Czechoslovak Mathematical Journal

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Let $G$ be a finite group. We prove that if every self-centralizing subgroup of $G$ is nilpotent or subnormal or a TI-subgroup, then every subgroup of $G$ is nilpotent or subnormal. Moreover, $G$ has either a normal Sylow $p$ -subgroup or a normal $p$ -complement for each prime divisor $p$ of $| G |$ .

Leibniz's rule on two-step nilpotent Lie groups

Krystian Bekała (2016)

Colloquium Mathematicae

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Let be a nilpotent Lie algebra which is also regarded as a homogeneous Lie group with the Campbell-Hausdorff multiplication. This allows us to define a generalized multiplication $f g = {(f^{\lor} * g^{\lor})}^{\land}$ of two functions in the Schwartz class (*), where $^{\lor}$ and $^{\land}$ are the Abelian Fourier transforms on the Lie algebra and on the dual * and ∗ is the convolution on the group . In the operator analysis on nilpotent Lie groups an important notion is the one of symbolic calculus which can be viewed as a higher order...

Sub-Laplacian with drift in nilpotent Lie groups

Camillo Melzi (2003)

Colloquium Mathematicae

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We consider the heat kernel $ϕ_{t}$ corresponding to the left invariant sub-Laplacian with drift term in the first commutator of the Lie algebra, on a nilpotent Lie group. We improve the results obtained by G. Alexopoulos in [1], [2] proving the “exact Gaussian factor” exp(-|g|²/4(1+ε)t) in the large time upper Gaussian estimate for $ϕ_{t}$ . We also obtain a large time lower Gaussian estimate for $ϕ_{t}$ .

An obstruction to homogeneous manifolds being Kähler

Bruce Gilligan (2005)

Annales de l’institut Fourier

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Let $G$ be a connected complex Lie group, $H$ a closed, complex subgroup of $G$ and $X : = G / H$ . Let $R$ be the radical and $S$ a maximal semisimple subgroup of $G$ . Attempts to construct examples of noncompact manifolds $X$ homogeneous under a nontrivial semidirect product $G = S ⋉ R$ with a not necessarily $G$ -invariant Kähler metric motivated this paper. The $S$ -orbit $S / S \cap H$ in $X$ is Kähler. Thus $S \cap H$ is an algebraic subgroup of $S$ [4]. The Kähler assumption on $X$ ought to imply the $S$ -action on the base $Y$ of any homogeneous fibration...