Jiajing Miao
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Jiajing Miao has a total of 8 co-authors. Here are the top co-authors by number of shared publications:
Haiming Liu
School of Mathematic Science, Mudanjiang Normal University, Mudanjiang 157011, China
3 shared publications- Haiming Liu
School of Mathematics Science, Mudanjiang Normal University, Mudanjiang 157011, China
3 shared publications - Jianyun Guan
Northeast Normal University, Changchun, P. R. China
3 shared publications - Han Zhang
School of Mathematics, Mudanjiang Normal University, Aimin, Mudanjiang, People’s Republic of China
1 shared publication Jinli Yang
Mudanjiang Normal Univ, Sch Math, Mudanjiang 157011, Peoples R China
1 shared publication- Jinli Yang
School of Mathematics, Mudanjiang Normal University, Mudanjiang 157011, China
1 shared publication
Latest Publications
- 14 November 2025
- Published by Springer Nature in Research in the Mathematical Sciences
- Vol. 12 (4) , 90
Biharmonic curve in roto-translation group
- 14 November 2025
- Published by Springer Nature in Research in the Mathematical Sciences
- Vol. 12 (4) , 90
Biharmonic curve in roto-translation group
- Open Access
- 1 January 2025
- Published by American Institute of Mathematical Sciences (AIMS) in Electronic Research Archive
- Vol. 33 (12) , 7676-7698
Perturbed Bott algebraic Schouten solitons on 3D Lorentzian Lie groups
In this paper, we defined and classified the algebraic Schouten solitons that are associated with the perturbed Bott connection on three-dimensional Lorentzian Lie groups possessing three distinct distributions. By transforming equations of perturbed Bott algebraic Schouten solitons into algebraic equations, we found that $ G_3, G_5, G_6 $, and $ G_7 $ have perturbed Bott algebraic Schouten solitons under the first distribution. $ G_3, G_6 $, and $ G_7 $ have such solitons under the second distribution. Additionally, $ G_2, G_3, G_4, G_5, G_6 $, and $ G_7 $ have such solitons under the third distribution.- 1 January 2025
- Published by American Institute of Mathematical Sciences (AIMS) in Electronic Research Archive
- Vol. 33 (12) , 7676-7698
Open AccessPerturbed Bott algebraic Schouten solitons on 3D Lorentzian Lie groups
In this paper, we defined and classified the algebraic Schouten solitons that are associated with the perturbed Bott connection on three-dimensional Lorentzian Lie groups possessing three distinct distributions. By transforming equations of perturbed Bott algebraic Schouten solitons into algebraic equations, we found that $ G_3, G_5, G_6 $, and $ G_7 $ have perturbed Bott algebraic Schouten solitons under the first distribution. $ G_3, G_6 $, and $ G_7 $ have such solitons under the second distribution. Additionally, $ G_2, G_3, G_4, G_5, G_6 $, and $ G_7 $ have such solitons under the third distribution. - Open Access
- 1 January 2023
- Published by American Institute of Mathematical Sciences (AIMS) in Communications in Analysis and Mechanics
- Vol. 15 (4) , 763-791
Algebraic Schouten solitons of Lorentzian Lie groups with Yano connections
In this paper, we discuss the beingness conditions for algebraic Schouten solitons associated with Yano connections in the background of three-dimensional Lorentzian Lie groups. By transforming equations of algebraic Schouten solitons into algebraic equations, the existence conditions of solitons are found. In particular, we deduce some formulations for Yano connections and related Ricci operators. Furthermore, we find the detailed categorization for those algebraic Schouten solitons on three-dimensional Lorentzian Lie groups. The major results demonstrate that algebraic Schouten solitons related to Yano connections are present in $ G_{1} $, $ G_{2} $, $ G_{3} $, $ G_{5} $, $ G_{6} $ and $ G_{7} $, while they are not identifiable in $ G_{4} $.- 1 January 2023
- Published by American Institute of Mathematical Sciences (AIMS) in Communications in Analysis and Mechanics
- Vol. 15 (4) , 763-791
Open AccessAlgebraic Schouten solitons of Lorentzian Lie groups with Yano connections
In this paper, we discuss the beingness conditions for algebraic Schouten solitons associated with Yano connections in the background of three-dimensional Lorentzian Lie groups. By transforming equations of algebraic Schouten solitons into algebraic equations, the existence conditions of solitons are found. In particular, we deduce some formulations for Yano connections and related Ricci operators. Furthermore, we find the detailed categorization for those algebraic Schouten solitons on three-dimensional Lorentzian Lie groups. The major results demonstrate that algebraic Schouten solitons related to Yano connections are present in $ G_{1} $, $ G_{2} $, $ G_{3} $, $ G_{5} $, $ G_{6} $ and $ G_{7} $, while they are not identifiable in $ G_{4} $. - Open Access
Classification of Lorentzian Lie Groups Based on Codazzi Tensors Associated with Yano Connections
In this paper, we derive the expressions of Codazzi tensors associated with Yano connections in seven Lorentzian Lie groups. Furthermore, we complete the classification of three-dimensional Lorentzian Lie groups in which Ricci tensors associated with Yano connections are Codazzi tensors. The main results are listed in a table, and indicate that and do not have Codazzi tensors associated with Yano connections, , , , and have Codazzi tensors associated with Yano connections.Open AccessClassification of Lorentzian Lie Groups Based on Codazzi Tensors Associated with Yano Connections
In this paper, we derive the expressions of Codazzi tensors associated with Yano connections in seven Lorentzian Lie groups. Furthermore, we complete the classification of three-dimensional Lorentzian Lie groups in which Ricci tensors associated with Yano connections are Codazzi tensors. The main results are listed in a table, and indicate that and do not have Codazzi tensors associated with Yano connections, , , , and have Codazzi tensors associated with Yano connections. - Open Access
Extended Legendrian Dualities Theorem in Singularity Theory
In this paper, we find some new information on Legendrian dualities and extend them to the case of Legendrian dualities for continuous families of pseudo-spheres in general semi-Euclidean space. In particular, we construct all contact diffeomorphic mappings between the contact manifolds and display them in a table that contains all information about Legendrian dualities.
Open AccessExtended Legendrian Dualities Theorem in Singularity Theory
In this paper, we find some new information on Legendrian dualities and extend them to the case of Legendrian dualities for continuous families of pseudo-spheres in general semi-Euclidean space. In particular, we construct all contact diffeomorphic mappings between the contact manifolds and display them in a table that contains all information about Legendrian dualities.
- Open Access
- 2 June 2021
- Published by Wiley in Journal of Mathematics
- Vol. 2021, 1-22
The Sub-Riemannian Limit of Curvatures for Curves and Surfaces and a Gauss–Bonnet Theorem in the Rototranslation Group
The rototranslation group ℛ T is the group comprising rotations and translations of the Euclidean plane which is a 3-dimensional Lie group. In this paper, we use the Riemannian approximation scheme to compute sub-Riemannian limits of the Gaussian curvature for a Euclidean C 2 -smooth surface in the rototranslation group away from characteristic points and signed geodesic curvature for Euclidean C 2 -smooth curves on surfaces. Based on these results, we obtain a Gauss–Bonnet theorem in the rototranslation group.
- 2 June 2021
- Published by Wiley in Journal of Mathematics
- Vol. 2021, 1-22
Open AccessThe Sub-Riemannian Limit of Curvatures for Curves and Surfaces and a Gauss–Bonnet Theorem in the Rototranslation Group
The rototranslation group ℛ T is the group comprising rotations and translations of the Euclidean plane which is a 3-dimensional Lie group. In this paper, we use the Riemannian approximation scheme to compute sub-Riemannian limits of the Gaussian curvature for a Euclidean C 2 -smooth surface in the rototranslation group away from characteristic points and signed geodesic curvature for Euclidean C 2 -smooth curves on surfaces. Based on these results, we obtain a Gauss–Bonnet theorem in the rototranslation group.
- Open Access
- 1 January 2021
- Published by American Institute of Mathematical Sciences (AIMS) in AIMS Mathematics
- Vol. 6 (8) , 8772-8791
Gauss-Bonnet theorem in Lorentzian Sasakian space forms
In this paper, we use a Lorentzian approximation scheme to compute the sub-Lorentzian limit of curvatures for curves and Lorentzian surfaces in the Lorentzian Bianci-Cartan-Vranceanu model of $ 3 $-dimensional Lorentzian Sasakian space forms. Based on these results, we get a Gauss-Bonnet theorem in the Lorentzian Sasakian space forms.
- 1 January 2021
- Published by American Institute of Mathematical Sciences (AIMS) in AIMS Mathematics
- Vol. 6 (8) , 8772-8791
Open AccessGauss-Bonnet theorem in Lorentzian Sasakian space forms
In this paper, we use a Lorentzian approximation scheme to compute the sub-Lorentzian limit of curvatures for curves and Lorentzian surfaces in the Lorentzian Bianci-Cartan-Vranceanu model of $ 3 $-dimensional Lorentzian Sasakian space forms. Based on these results, we get a Gauss-Bonnet theorem in the Lorentzian Sasakian space forms.
- Open Access
- 1 January 2021
- Published by American Institute of Mathematical Sciences (AIMS) in AIMS Mathematics
- Vol. 6 (4) , 3177-3204
Geometric invariants and focal surfaces of spacelike curves in de Sitter space from a caustic viewpoint
The focal surface of a generic space curve in Euclidean $ 3 $-space is a classical subject which is a two dimensional caustic and has Lagrangian singularities. In this paper, we define the first de Sitter focal surface and the second de Sitter focal surface of de Sitter spacelike curve and consider their singular points as an application of the theory of caustics and Legendrian dualities. The main results state that de Sitter focal surfaces can be seen as two dimensional caustics which have Lagrangian singularities. To characterize these singularities, a useful new geometric invariant $ \rho(s) $ is discovered and two dual relationships between focal surfaces and spacelike curve are given. Three examples are used to demonstrate the main results.- 1 January 2021
- Published by American Institute of Mathematical Sciences (AIMS) in AIMS Mathematics
- Vol. 6 (4) , 3177-3204
Open AccessGeometric invariants and focal surfaces of spacelike curves in de Sitter space from a caustic viewpoint
The focal surface of a generic space curve in Euclidean $ 3 $-space is a classical subject which is a two dimensional caustic and has Lagrangian singularities. In this paper, we define the first de Sitter focal surface and the second de Sitter focal surface of de Sitter spacelike curve and consider their singular points as an application of the theory of caustics and Legendrian dualities. The main results state that de Sitter focal surfaces can be seen as two dimensional caustics which have Lagrangian singularities. To characterize these singularities, a useful new geometric invariant $ \rho(s) $ is discovered and two dual relationships between focal surfaces and spacelike curve are given. Three examples are used to demonstrate the main results.