Yanlin Li

Yanlin Li
Hangzhou Normal University | HNU · Department of Mathematics

PhD

About

20
Publications
2,291
Reads
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224
Citations
Education
October 2016 - October 2017
Columbia University
Field of study
  • Mathematic
October 2014 - June 2016
Northeast Normal University
Field of study
  • Mathematic
September 2011 - June 2014
Northeast Normal University
Field of study
  • Mathematic

Publications

Publications (20)
Article
E. Study found that there is a one-to-one correspondence between the oriented lines in Euclidean three space and the dual points of the dual unit sphere in dual three space, and it has wide applications in Engineering. In this paper, we investigate a ruled surface as a curve on the dual unit sphere by using E. Study's theory. Then we define the not...
Article
We prove that if an η \eta -Einstein para-Kenmotsu manifold admits a conformal η \eta -Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a conformal η \eta -Ricci soliton is Einstein if its potential vector field V V is infinitesimal paracontact transformation or collinear with the Reeb vector field. Furthermore, we...
Article
Full-text available
In this article, we derive Chen’s inequalities involving Chen’s δ -invariant δM , Riemannian invariant δ(m1,⋯,mk) , Ricci curvature, Riemannian invariant Θk(2≤k≤m) , the scalar curvature and the squared of the mean curvature for submanifolds of generalized Sasakian-space-forms endowed with a quarter-symmetric connection. As an application of the ob...
Article
In this paper, we take advantage of envelope theory and singularity theory to study the evolutoids and pedaloids in Minkowski plane. We illustrate an internal correlation from algebraic and geometric viewpoints, and give the geometric explanation of evolutoids and pedaloids. Then, we generalize the notions of evolutoids and pedaloids to the categor...
Article
In the article, we present the best possible parameters \(\alpha ,\beta \) such that the double inequality $$\begin{aligned} S_{\alpha }(a,b)<T_{4}(a,b)<S_{\beta }(a,b) \end{aligned}$$holds for \(a, b>0\) with \(a\ne b\), and provide new bounds for the complete elliptic integral of the second kind, where \(S_{p}(a,b)\) and \(T_{4}(a,b)\) are the ge...
Article
Full-text available
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...
Article
Full-text available
Purpose Glioma is the most common type of primary brain tumor in adults, and it causes significant morbidity and mortality, especially in high‐grade glioma (HGG) patients. The accurate prognostic prediction of HGG is vital and helpful for clinicians when developing therapeutic strategies. Therefore, we propose a machine learning‐based survival pred...
Article
Full-text available
Localized nasopharyngeal cancer (NPC) is a highly curable disease, but the prognosis of certain cases is still poor. Distinguishing patients with a poor outcome is necessary when developing therapeutic strategies. The aim of this study was to investigate the characteristics of early death (ED) among patients with localized NPC, and to identify inde...
Article
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...
Preprint
The evolutes and pedal curves play an important role in classical differential geometry. It is make sense to study these interesting curves in the Minkowski plane. In this paper, we take the advantage of envelope theory and singularity theory to investigate the evolutes and pedal curves and extend these notions to the category of frontal curves in...
Article
This paper generalizes the tangent developables of regular curves with linear independent condition to the tangent developables of framed curves and investigates the singularities of tangent developables in Euclidean 3-space. In contrast to tangent developables of regular curves with linear independent condition, the tangent developables of framed...
Article
Full-text available
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...
Article
For the spherical unit speed nonlightlike curve in pseudo-hyperbolic space and de Sitter space [Formula: see text] and a given point P, we can define naturally the pedal curve of [Formula: see text] relative to the pedal point P. When the pseudo-sphere dual curve germs are nonsingular, singularity types of such pedal curves depend only on locations...
Article
Full-text available
We consider the differential geometry of evolutes of singular curves and give the definitions of spacelike fronts and timelike fronts in the Minkowski plane. We also give the notions of moving frames along the non‐lightlike fronts in the Minkowski plane. By using the moving frames, we define the evolutes of non‐lightlike fronts and investigate the...
Preprint
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.
Preprint
Full-text available
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...
Article
In this paper, we introduce a one-parameter family of Legendre curves in the unit spherical bundle over the unit sphere and the curvature. We give the existence and uniqueness theorems for one-parameter families of spherical Legendre curves by using the curvatures. Then we define an envelope for the one-parameter family of Legendre curves in the un...
Article
Full-text available
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...
Article
Full-text available
Notions of the pedal curves of regular curves are classical topics. T. Nishimura [T. Nishimura, Demonstratio Math., 43 (2010), 447-459] has done some work associated with the singularities of pedal curves of regular curves. But if the curve has singular points, we can not define the Frenet frame at these singular points. We also can not use the Fre...

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