Shaoqiang Deng

activity

20082026

most citedEven dimensional homogeneous Finsler spaces with positive flag curvature

12 citations · 59 across the 29 of their papers we have counts for

collaborators

33 papers

math.DG2026

An Adjoint Criterion for Left-Invariant $m$ -Modified Conformal Vector Fields on Even-Dimensional Lie Groups

Zhigang Li, Shaoqiang Deng, Hui Zhang

For a fixed positive real constant $m$ , a real Lie algebra of even dimension $2 k$ admits a nonzero left-invariant $m$ -modified conformal vector field for some nondegenerate metric…

math.DG2026

Infinitely many closed geodesic images on simply connected compact rank-one symmetric spaces

Zhiqi Chen, Shaoqiang Deng, Hui Zhang

We prove that every smooth Riemannian metric on the underlying smooth manifold of a simply connected compact rank-one symmetric space, namely $S^{n}$ $(n \geq 2)$ , $\CP^m$ $(m \geq 1)$ , $\…

math.DG2026

Positive sectional curvature on a family of exotic fifteen-sphere

Zhiqi Chen, Shaoqiang Deng, Hui Zhang

We construct Riemannian metrics of strictly positive sectional curvature on at least 508 pairwise nondiffeomorphic exotic fifteen-spheres, without distinguishing orientations. The…

math.DG2026

Positive sectional curvature and non-isometric circle actions on a family of eleven-spheres

Shaoqiang Deng, Zhiguang Hu, Hui Zhang

We study the construction of positively curved Riemannian metrics by non-isometric circle actions. For a family of homotopy eleven-spheres whose Eells--Kuiper invariants form the e…

math.DG2026

A diameter gap for irreducible compact symmetric spaces of fixed rank

Zhiqi Chen, Shaoqiang Deng, Hui Zhang

We prove that, for every positive integer $r$ , the positive normalized diameters of isometric quotients of simply connected irreducible compact Riemannian symmetric spaces of rank…

math.DG2025

A counter example for the Homogeneity Conjecture

Ming Xu, Shaoqiang Deng

We construct a counter example to show that the Homogeneity Conjecture, first proposed by J.A. Wolf in 1962, is not true. To be precise, we prove that on the Lie group Sp(2), there…

math-ph2022

Polyubles, Poisson homogeneous spaces and multi-flag varieties

Shaoqiang Deng, Chuangchuang Kang, Shizhuo Yu

A polyuble of a Manin triple can be regarded as the `` $n$ -th power'' of it, which plays an important rule in the study of Poisson geometry, mathematical physics and Lie theory. In…

math.DG2018★ 2 cited

Geodesic orbit Finsler metrics on Euclidean spaces

Ming Xu, Shaoqiang Deng, Zaili Yan

A Finsler space $(M, F)$ is called a geodesic orbit space if any geodesic of constant speed is the orbit of a one-parameter subgroup of isometries of $(M, F)$ . In this paper, we stu…

math.DG2017

Non-naturally reductive Einstein metrics on normal homogeneous Einstein manifolds

Zaili Yan, Shaoqiang Deng

It is an important problem in differential geometry to find non-naturally reductive homogeneous Einstein metrics on homogeneous manifolds. In this paper, we consider this problem f…

math.DG2017

Non-naturally reductive Einstein metrics on $SO (n)$

Huibin Chen, Zhiqi Chen, Shaoqiang Deng

In this article, we prove that every compact simple Lie group $S O (n)$ for $n \geq 10$ admits at least $2 ([\frac{n - 1}{3}] - 2)$ non-naturally reductive left-invariant Einste…

math.DG2017★ 1 cited

New Non-naturally reductive Einstein metrics on Exceptional simple Lie groups

Huibin Chen, Zhiqi Chen, ShaoQiang Deng

In this article, we achieved several non-naturally reductive Einstein metrics on exceptional simple Lie groups, which are formed by the decomposition arising from general Wallach s…

math.DG2016

Recent progress on homogeneous Finsler spaces with positive curvature

Shaoqiang Deng, Ming Xu

This is a survey paper on our recent works concerning the classification of positively curved homogeneous Finsler spaces, and some related topics. At the final part, we present som…

math.DG2016

Geodesic and curvature of piecewise flat Finsler surfaces

Ming Xu, Shaoqiang Deng

A piecewise flat Finsler metric on a triangulated surface $M$ is a metric whose restriction to any triangle is a flat triangle in some Minkowski space with straight edges. One of t…

math.DG2016

Locally 2-fold symmetric manifolds are locally symmetric

Shaoqiang Deng, Vladimir S. Matveev

A manifold is locally \emph{ $k$ -fold symmetric}, if for any point and any $k$ -dimensional vector subspace tangent to this point there exists a local isometry such that this point i…

math.DG2016

Rigidity of negatively curved geodesic orbit Finsler spaces

Ming Xu, Shaoqiang Deng

We prove some rigidity results on geodesic orbit Finsler spaces with non-positive curvature. In particular, we show that a geodesic Finsler space with strictly negative flag curvat…

math.DG2016★ 7 cited

Homogeneous Finsler spaces and the flag-wise positively curved condition

Ming Xu, Shaoqiang Deng

In this paper, we introduce the flag-wise positively curved condition for Finsler spaces (the (FP) Condition), which means that in each tangent plane, we can find a flag pole in th…

math.DG2015★ 2 cited

Towards the classification of odd dimensional homogeneous reversible Finsler spaces with positive flag curvature

Ming Xu, Shaoqiang Deng

In this paper, we use the flag curvature formula for homogeneous Finsler spaces in our previous work to classify odd dimensional smooth coset spaces admitting positively curved rev…

math.DG2015★ 1 cited

Homogeneous $(α, β)$ -spaces with positive flag curvature and vanishing S-curvature

Ming Xu, Shaoqiang Deng

We give a complete classification of homogeneous $(α, β)$ -metrics with positive flag curvature and vanishing S-curvature.

math.DG2014★ 6 cited

Normal homogeneous Finsler spaces

Ming Xu, Shaoqiang Deng

In this paper, we study normal homogeneous Finsler spaces. We first define the notion of a normal homogeneous Finsler space, using the method of isometric submersion of Finsler met…

math.DG2014★ 12 cited

Even dimensional homogeneous Finsler spaces with positive flag curvature

Ming Xu, Shaoqiang Deng, Libing Huang +1

In this paper, we use the technique of Finslerian submersion to deduce a flag curvature formula for homogeneous Finsler spaces. Based on this formula, we give a complete classifica…

math.DG2014★ 1 cited

The Landsberg equation of a Finsler space

Ming Xu, Shaoqiang Deng

Given a Finsler space, we introduce a system of partial differential equations, called the Landsberg equation. Based on a careful analysis of the Landsberg equation and the observa…

math.DG2014

$(α_{1}, α_{2})$ -Spaces and Clifford-Wolf Homogeneity

Ming Xu, Shaoqiang Deng

In this paper, we introduce a new type of Finsler metrics, called $(α_{1}, α_{2})$ -metrics. We define the notion of the good datum of a homogeneous $(α_{1}, α_{2})$ -metric and use that to st…

math.DG2013

Clifford-Wolf homogeneous Finsler metrics on spheres

Ming Xu, Shaoqiang Deng

An isometry of a Finsler space is called Clifford-Wolf translation (CW-translation) if it moves all points the same distance. A Finsler space $(M, F)$ is called Clifford-Wolf homog…

math.DG2013★ 1 cited

Killing frames and S-curvature of homogeneous Finsler spaces

Ming Xu, Shaoqiang Deng

In this paper, we first deduce a formula of S-curvature of homogeneous Finsler spaces in terms of Killing vector fields. Then we prove that a homogeneous Finsler space has isotropi…

An Adjoint Criterion for Left-Invariant m-Modified Conformal Vector Fields on Even-Dimensional Lie Groups

Infinitely many closed geodesic images on simply connected compact rank-one symmetric spaces

Positive sectional curvature on a family of exotic fifteen-sphere

Positive sectional curvature and non-isometric circle actions on a family of eleven-spheres

A diameter gap for irreducible compact symmetric spaces of fixed rank

A counter example for the Homogeneity Conjecture

Polyubles, Poisson homogeneous spaces and multi-flag varieties

Geodesic orbit Finsler metrics on Euclidean spaces

Non-naturally reductive Einstein metrics on normal homogeneous Einstein manifolds

Non-naturally reductive Einstein metrics on SO(n)

New Non-naturally reductive Einstein metrics on Exceptional simple Lie groups

Recent progress on homogeneous Finsler spaces with positive curvature

Geodesic and curvature of piecewise flat Finsler surfaces

Locally 2-fold symmetric manifolds are locally symmetric

Rigidity of negatively curved geodesic orbit Finsler spaces

Homogeneous Finsler spaces and the flag-wise positively curved condition

Towards the classification of odd dimensional homogeneous reversible Finsler spaces with positive flag curvature

Homogeneous (α,β)-spaces with positive flag curvature and vanishing S-curvature

Normal homogeneous Finsler spaces

Even dimensional homogeneous Finsler spaces with positive flag curvature

The Landsberg equation of a Finsler space

(α1​,α2​)-Spaces and Clifford-Wolf Homogeneity

Clifford-Wolf homogeneous Finsler metrics on spheres

Killing frames and S-curvature of homogeneous Finsler spaces

An Adjoint Criterion for Left-Invariant $m$ -Modified Conformal Vector Fields on Even-Dimensional Lie Groups

Non-naturally reductive Einstein metrics on $SO (n)$

Homogeneous $(α, β)$ -spaces with positive flag curvature and vanishing S-curvature

$(α_{1}, α_{2})$ -Spaces and Clifford-Wolf Homogeneity