# Zhigang WangHarbin Normal University | HRBNU · Mathematics

Zhigang Wang

Professor

## About

36

Publications

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344

Citations

Introduction

## Publications

Publications (36)

In this paper, we consider two kinds of developable surfaces along a timelike frontal curve lying in a timelike surface in Minkowski 3-space, the Lorentz–Darboux rectifying surfaces and the Lorentz–Darboux osculating surfaces. Meanwhile, we also consider two curves generated by such a timelike frontal curve. We give two new invariants of the fronta...

In this paper, we consider the local topological structures of a class of new worldsheets, call it the rectifying worldsheets, which are generated by a class of singular worldlines. Using the classification approaches of the finite type on the tangent developables and defining the extended striction curve, this paper gives the detailed classificati...

The main work of this paper is to investigate two kinds of generalized focal surfaces and two kinds of evolutes generated by spacelike curve γ lying in lightlike surfaces in Minkowski three‐space. Applying the method of unfolding theory in singularity theory to our study, it is shown that there exist the cuspidal edge and the swallowtail types of s...

Singular ruled surface is an interesting research object and is the breakthrough point of exploring new problems. However, because of singularity, it’s difficult to study the properties of singular ruled surfaces. In this paper, we combine singularity theory and Clifford algebra to study singular ruled surfaces. We take advantage of the dual number...

Developable surfaces are the special ruled surfaces where the Gaussian curvature of each point vanishes. Tangent developable is the most interesting surface among three fundamental types of developable surfaces. This paper investigates lightlike tangent developable generated by a lightlike base curve in de Sitter 3-space. We first give the topologi...

In this paper, we consider the sequence of the principal‐directional curves of a curve γ and define the slant helix of order n (n‐SLH) of the curve in Euclidean 3‐space. The notion is an extension of the notion of slant helix. We present an important formula that determines if the nth principal‐directional curve of γ can be the slant helix of order...

In this paper, by introducing a new frame on spacelike curves lying in lightcone 3‐space, we investigate the geometric properties of the lightlike surface of the Darboux‐like indicatrix and the lightlike surface of the binormal indicatrix generated by spacelike curves in lightcone 3‐space. As an extension of our previous work and an application of...

Choosing an alternative frame, which is the Frenet frame of the principal‐directional curve along a nonlightlike Frenet curve γ, we define de Sitter Darboux images, hyperbolic Darboux images, and lightcone images generated by the principal directional curves of nonlightlike Frenet curves and investigate geometric properties of these associated curv...

Confining the traveling trajectory of a tachyon to the two-dimensional Lorentzian space forms, we describe the trajectory as a spacelike front in these Lorentzian space forms. Introducing the differential geometry of singular curves in Lorentzian space forms, that is, the hyperbolic space and de Sitter space, and applying the Legendrian duality the...

In this paper, we study the pedal curves and evolutes of curves in the sphere from the view point of envelope theory and singularity theory. We give the definitions and relationships between the pedaloids and evolutoids of curves in the sphere. Furthermore, we extend these notions and relationships to the frontal curves in the sphere.

In this paper, we consider the sequence of the principal-directional curves of a curve γ and define the slant helix of order n (n-SLH) of the curve in Euclidean 3-space, the notion is an extension of the notion of slant helix presented by S. Izumiya and N. Takeuchi. We present an important formula to examine if the nth principal-directional curve o...

In this paper, we consider spacelike curves in the light-cone 3-space that is canonically embedded in the light-cone 4-space and the de Sitter 4-space in Minkowski 5-space. To study the differential geometry of spacelike curves in the light cone, we propose a new type of frame, called the light-cone frame, moving along a spacelike curve. Concerning...

In this paper, we introduce three kinds of tubular surfaces associated to original center curves í µí¼¸lyingµí¼¸lying in spacelike surfaces in Lorentz-Minkowski 3-space. It is demonstrated that these tubular surfaces can occur some singularities and the types of these singularities can be characterised by several invariants, respectively. Some inte...

In this paper, as applications of singularity theory, we study the singularities of several worldsheets generated by null Cartan curves in Lorentz-Minkowski space-time. Using the approach of the unfolding theory in singularity theory, we establish the relationships between these worldsheets and invariants such that the cuspidal edge type of singula...

In this paper, the singularities of the geometry for four classes of worldsheets, which are respectively, located in three-dimensional hyperbolic space and three-dimensional de Sitter space–time are considered. Under the theoretical frame of geometry of space–time and as applications of singularity theory, it is shown that these worldsheets have tw...

In this paper, a class of indefinite hypersurfaces and a class of indefinite surfaces generated by timelike curves located in nullcone in 4-dimensional semi-Euclidean space with index 2 are discussed. Using the unfolding theory in singularity theory, the singularities of the indefinite hypersurfaces and the indefinite surfaces are classified and th...

In this paper, we consider the null surfaces of null Cartan curves in Anti-de Sitter 3-space and making use of singularitytheory, we classify the singularities of the null surfaces and investigate the relationships between singularities of the null surfacesand differential geometric invariants of null Cartan curves in Anti-de Sitter 3-space. Finall...

As an extension of the class of ( α , ψ ) -Meir-Keeler-Khan single-valued mappings defined by Redjel et al., a new type of ( α , ψ ) -Meir-Keeler-Khan multivalued mappings is presented. Fixed point theorems and endpoints theorems are established on such mappings. Some main results by Redjel et al. and Khan et al. are extended and generalized.
MSC:...

The theory of the Legendrian singularity is applied for lightcones that are canonically embedded in the higher-dimensional lightcone and de Sitter space in the Minkowski space-time. The singularities of two classes of hypersurfaces that are dual to space-like hypersurface in the lightcone under Legendrian dualities are analyzed in detail.

By establishing some differential geometry theory on the 1-lightlike surfaces, we show several geometric properties of the 1-lightlike surfaces which are completely different from non-lightlike surfaces. Based on these theories, we consider the singularities of the 1-lightlike surfaces in semi- Euclidean 4-space with index two as an application of...

In this paper, a new concept of generalized quasi-partial metric spaces is presented. Some fixed point results due to Karapinar et. al., [E. Karapinar, I. M. Erhan, A. Öztürk, Math. Comput. Modelling, 57 (2013), 2442-2448] are extended in the setting of the generalized quasi-partial metric spaces.

We generalize the deterministic and the stochastic single-group SIRS epidemic models with saturated incidence rate introduced by Lahrouz, Omari, and Kiouach to the multi-group versions. In the deterministic multi-group model, the fact is highlighted that if the threshold (Formula presented.), then the infective condition disappears and it means the...

In this paper, as a type of event horizons in astrophysics, a class of lightlike hypersurfaces that is generated by null curves will be investigated and discussed. Based on discussions of the properties of the local differential geometry of null curves and singularity theory, we provide classifications of the singularities of lightlike hypersurface...

In this paper, we extend the deterministic single-group MSIRS epidemic model to a multi-group model, and we also extend the deterministic multi-group framework to a stochastic one and formulate it as a stochastic differential equation. In the deterministic multi-group model, the basic reproduction number R-0 is a threshold that completely determine...

In this paper, we consider the null curves in the 3-nullcone with index
2 and we investigate these curves in the framework of the theory of
Legendrian dualities between nullcones. The sufficient and necessary
conditions for the classifications of the singularities of both Gaussian
surfaces and those nullcone dual surfaces that are associated with a...

In this paper, we discuss multigroup SEIQR (susceptible, exposed, infectious, quarantined, and recovered) models with and without random perturbation in computer network. The transmission of malicious objects in computer network is formulated in these two models. In the deterministic model, the basic reproduction number R-0 is a threshold which com...

In this paper we investigate the differential geometry of 1-lightlike submanifolds in anti-de Sitter n-space as an application of the theory of Legendrian singularities. Based on some theory of lightlike submanifolds, we also introduce the notion of 1-lightlike horospherical Gauss curvature, which is important for us to study the singularities of 1...

An SEIR epidemic model with constant immigration and random fluctuation around the endemic equilibrium is considered. As a special case, a deterministic system discussed by Li et al. will be incorporated into the stochastic version given by us. We carry out a detailed analysis on the asymptotic behavior of the stochastic model, also regarding of th...

In this paper, we investigate the null developables of timelike curves that lie on nullcone in 3-dimensional semi-Euclidean space with index 2. We classify the singularities of the null developables of timelike curves. The primary approach is based on the classical unfolding theory in singularity theory, which has been extensively applied in studyi...

We explore the dynamics of a class of mutualism-competition-predator interaction models with Beddington-DeAngelis functional responses and impulsive perturbations. Sufficient conditions for existence of positive periodic solution are established by using a continuation theorem in coincidence degree theory, which have been extensively applied in stu...

We discuss a two-group SEIR epidemic model with distributed delays, incorporating random fluctuation around the endemic equilibrium. Our research shows that the endemic equilibrium of the model with distributed delays and random perturbation is stochastically asymptotically stable in the large. In addition, a sufficient stability condition is obtai...

Singularities of the focal surfaces and the binormal indicatrix associated with a null Cartan curve will be investigated in Minkowski 3-space. The relationships will be revealed between singularities of the above two subjects and differential geometric invariants of null Cartan curves; these invariants are deeply related to the order of contact of...

Singularities of null Darboux developable, Gaussian surfaces and pseudo-spherical Darboux images associated with a null Cartan curve will be investigated in Minkowski 3-space. The relationships will be revealed between singularities of the above three subjects and differential geometric invariants of null Cartan curves, these invariants are deeply...

In this Letter, we investigate the ruled null surfaces of the principal normal indicatrix of a null Cartan curve in de Sitter 3-space, an important vacuum solution to Einstein's equations of general relativity with cosmological terms. We classify the singularities of the ruled null surfaces and reveal the relationships between the singularities of...