Yong Wang
In this paper, we define and classify minimal translation surfaces with respect to a kind of semi-symmetric metric connections and a kind of semi-symmetric non-metric connections in $\mathbb{R}^3$ and $\mathbb{R}^3_1$.
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In this paper, we study and classify singular minimal translation surfaces in a Euclidean space of dimension 3 endowed with a certain semi-symmetric (non-)metric connection.
Natural parallel translation and connection associated to navigation data
本文提出一种基于黎曼平行性的自然平行翻译方法，用于处理导航数据的几何特性，保持Finsler范数并具有有限维holonomy群。
Classification of translation surfaces in $\mathbb{R}^3$ with constant sectional curvature
本文研究赋予典范半对称非度量联络的欧氏空间中的平移曲面，完成常截面曲率平移曲面的完全分类，证明其为广义柱面，同时指出该框架下存在截面曲率可常可非常的广义柱面，与Levi-Civita联络情形存在差异。
We prove some estimates of the volumes of the sets of translation surfaces of unit area having several independent small saddle connections in a rank one affine submanifold.
In this paper, we define the semi-symmetric metric connection on super Riemannian manifolds. We compute the semi-symmetric metric connection and its curvature tensor and its Ricci tensor on super warped product spaces. We introduce two kind of super warped product spaces with the semi-symmetric metric connection and give the conditions under which these two super warped product spaces with the semi-symmetric metric connection are the Einstein super spaces with the semi-symmetric metric connection.
The authors first in this paper define a semi-symmetric metric non-holonomic connection (called in briefly a semi-sub-Riemannian connection) on sub-Riemannian manifolds, and study the relations between sub-Riemannian connections and semi-sub-Riemannian connections. An invariant under a connection transformation $\nabla\rightarrow D$ is obtained. The authors then further deduce a sufficient and necessary condition that a sub-Riemannian manifold associated with a semi-sub-Riemannian connection is flat, and derive that a sub-Riemannian manifold with vanishing curvature with respect to semi-sub-Ri…
In this paper, we define a semi-symmetric non-metric connection on super Riemannian manifolds. And we compute the curvature tensor and the Ricci tensor of a semi-symmetric non-metric connection on super warped product spaces. Next, we introduce two kinds of super warped product spaces with a semi-symmetric non-metric connection and give the conditions that two super warped product spaces with a semi-symmetric non-metric connection are the Einstein super spaces with a semi-symmetric non-metric connection.
We classify the affine connections on compact orientable surfaces for which the pseudogroup of local isometries acts transitively. We prove that such a connection is either torsion-free and flat, the Levi-Civita connection of a Riemannian metric of constant curvature or the quotient of a translation-invariant connection in the plane.
The aim of the present paper is to study the properties of Riemannian manifolds equipped with a projective semi-symmetric connection.
Holomorphic projective connections on compact complex threefolds
本文分类复射影三维流形上的全纯射影联络，证明其若非平坦则必位于阿贝尔三维流形上，并排除平凡典范线丛的单连通紧复三维流形存在此类联络。
The object of this paper is to obtain the concircular curvature tensor of the semi symmetric non-metric connection on the Weyl manifold and to give a necessary and sufficient condition for a semi symmetric non-metric connection to be S-concircular.
In this paper, we study non integrable distributions in a Riemannian manifold with a semi-symmetric metric connection, a semi-symmetric non-metric connection and a statistical connection. We obtain the Gauss, Codazzi, and Ricci equations for non integrable distributions with respect to the semi-symmetric metric connection, the semi-symmetric non-metric connection and the statistical connection. As applications, we obtain Chen's inequalities for non integrable distributions of real space forms endowed with a semi-symmetric metric connection and a semi-symmetric non-metric connection. We give so…
In this paper, we define a semi-symmetric metric Killing vector field, then study semi-symmetric metric Killing vector fields on warped and multiply warped products with a semi-symmetric metric connection. We also study Killing and 2-Killing vector fields on multiply warped products.
In this paper, we obtain Chen's inequalities for submanifolds in $(κ,μ)$-contact space form with two kinds of generalized semi-symmetric non-metric connections.
The aim of this paper is to study generalized recurrent, generalized Ricci-recurrent, weakly symmetric and weakly Ricci-symmetric Kenmotsu manifolds with respect to the semi-symmetric non-metric connection.
The object of the present paper is to study locally $ϕ$-symmetric LP-Sasakian manifolds admitting semi-symmetric metric connection and obtain a necessary and sufficient condition for a locally $ϕ$-symmetric LP-Sasakian manifold with respect to semi-symmetric metric connection to be locally $ϕ$-symmetric LP-Sasakian manifold with respect to Levi-Civita connection.
Invariant and screen semi-invariant lightlike submanifolds of a metallic semi-Riemannian manifold with a quarter symmetric non-metric connection
本文在金属半黎曼流形上引入带四分之一对称非度量联络的不变与屏幕半不变类光子流形，刻画其分布的可积性与平行性，并给出全测地叶理的结果。
Constructions of Frenet Curves with respect to Semi-Symmetric Metric Connection
本文基于半对称度量连接，研究了三维流形中Frenet曲线的构造及其在不同流形中的示例。
In this paper, we study the doubly warped product manifolds with semisymmetric metric connection. We derive the curvatures formulas for doubly warped product manifold with semi-symmetric metric connection in terms of curvatures of components of doubly warped product manifolds. We also prove the necessary and sufficient condition for a doubly warped product manifold to be a warped product manifold. We obtain some results for Einstein doubly warped product manifold and Einstein-like doubly warped product manifold of class A with respect to a semi-symmetric metric connection.
Spacetime is a 4-dimensional connected Lorentzian manifold. In this paper, we extend the Levi-Civita connection in the definition of spacetime to the semi-symmetric non-metric connection and conclude geometric structures admitted by the metric (1.1) with the semi-symmetric non-metric connections. Obviously, Morris-Thorne spacetime is Ricci generalized pseudosymmetry, Ricci generalized projectively pseudosymmetry, and has conformal 2-forms that are recurrent, etc. It also is an Einstein manifold of level 2 and 3-quasi-Einstein manifold.
K-contact manifolds admitting some geometric solitons with Semi-Symmetric Non-Metric Connection
本文研究K-接触流形上具有半对称非度量联络的几何性质，引入相关向量场，探讨Riemann、共形Ricci及共形$\eta$-Ricci-Yamabe孤子，并给出流形为多种半对称的充要条件。
Investigations on a Riemannian manifold with a semi-symmetric non-metric connection and gradient solitons
本文研究具有半对称非度量联络的三维黎曼流形，构造存在性例子，并证明梯度 Ricci 孤立子、梯度 Yamabe 孤立子、Einstein 孤立子及 m-拟 Einstein 孤立子条件下的曲率或平凡性结论。
The present paper deals with some results of almsot semi-invariant submanifolds of generalized Sasakian-space-forms in \cite{ALEGRE3} with respect to semisymmetric metric connection, semisymmetric non-metric connection, Schouten-van Kampen connection and Tanaka-Webster connection.
Let $(M,F)$ be a connected Finsler space. An isometry of $(M,F)$ is called a Clifford-Wolf translation (or simply CW-translation) if it moves all points the same distance. The compact Finsler space $(M,F)$ is called restrictively Clifford-Wolf homogeneous (restrictively CW-homogeneous) if for any two sufficiently close points $x_1,x_2\in M$, there exists a CW-translation $σ$ such that $σ(x_1)=x_2$. In this paper, we define the good normalized datum for a homogeneous non-Riemannian $(α,β)$-space, and use it to study the restrictive CW-homogeneity of left invariant $(α,β)$-metrics on a compact c…
On riemannian connections and semi-simplicity of a Lie algebra
本研究利用spray定义的殆积结构，给出无挠线性联络为黎曼联络及可投影向量场李代数半单性的充要条件，并证明有限维李代数半单性的多个等价表述。
Characterizations of a Lorentzian Manifold with a semi-symmetric metric connection
研究带半对称度量联络的洛伦兹流形的刻画，通过分析曲率张量、Ricci张量等性质，得出其为完美流体时空、广义Robertson-Walker时空等结论，并将该联络应用于Ricci孤立子研究。
The present paper is composed of two parts. In the first one we define two pseudo-metrics $L_F$ and $K_F$ on the Teichmuüller space of semi-translation surfaces $\mathcal{TQ}_g(\underline k,ε)$, which are the symmetric counterparts to the metrics defined by William Thurston on $\mathcal{T}_g^n$. We prove some nice properties of $L_F$ and $K_F$, most notably that they are complete pseudo-metrics. In the second part we define their asymmetric analogues $L_F^a$ and $K_F^a$ on $\mathcal{T Q}_g^{(1)}(k, ε)$ and prove that their equality depends on two statements regarding 1-Lipschitz maps between p…
Given a semi-Hamiltonian system, we construct an $F$-manifold with a connection satisfying a suitable compatibility condition with the product. We exemplify this procedure in the case of the so-called $ε$-system. The corresponding connection turns out to be flat, and the flat coordinates give rise to additional chains of commuting flows
Semi-stability and local wall-crossing for hermitian Yang-Mills connections
本文在紧致凯勒流形上半稳定全纯向量丛的分次对象自同构群为阿贝尔群的条件下，给出极化邻域的半代数腔室分解，并证明稳定腔室中HYM联络收敛到分次对象上的HYM联络。
A semi-symmetric metric connection, perfect fluid space-time and phantom barrier
研究半对称度量连接在完美流体时空中的应用，探讨其作为Einstein型流形的条件，并证明完美流体时空的标量曲率恒定，从而推导出Einstein流形。
A review of the parallel transport (translation) in fibre bundles is presented. The connections between transports along paths and parallel transports in fibre bundles are examined. It is proved that the latter ones are special cases of the former.
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