arXiv subjects

Peilong Dong

Publications and source records attributed to Peilong Dong.

4 recordsLinked to original sources

arXiv2022

Isoparametric hypersurfaces and hypersurfaces with constant principal curvatures in Finsler spaces

In this paper, we study the relationship between isoparametric hypersurfaces and hypersurfaces with constant principal curvatures in Finsler spaces. We give some examples of isoparametric hypersurfaces with (non)constant principal curvatures on Randers manifolds with nonconstant flag curvatures. Furthermore, we construct an example of a conformally flat Randers manifold which admits a family of nonisoparametric hyperplanes with constant principal curvatures.

math.DG↗

arXiv2022

Isoparametric hypersurfaces of conic Finsler manifolds

In this paper, we introduce isoparametric functions and isoparametric hypersurfaces in conic Finsler spaces. We find that in a conic Minkowski space, besides the conic Minkowski hyperplanes, conic Minkowski hyperspheres and conic Minkowski cylinders, which are all isoparametric hypersurfaces, there are probably other isoparametric hypersurfaces, such as helicoids. Moreover, we give a complete classification of isoparametric hypersurfaces in kropina spaces with constant flag curvature.

math.DG↗

arXiv2020

Isoparametric hypersurfaces in Randers space forms

In this paper, we discuss anisotropic submanifolds and isoparametric hypersurfaces in a Randers space form (N,F) with the navigation datum (h,W). We find that (N, F) with respect to the BH-volume and (N,h) have the same isoparametric hypersurfaces although, in general, their isoparametric functions are different. This implies that the classification of isoparametric hypersurfaces in a Randers space form is the same as that in Riemannian case. Lastly, we give some examples of isoparametric functions in Randers space forms.

math.DG↗

arXiv2017

Weakly integrable Camassa-Holm-type equations

Series of deformed Camassa-Holm-type equations are constructed using the Lagrangian deformation and Loop algebra splittings. They are weakly integrable in the sense of modified Lax pairs.

nlin.SI↗