57 citations · 77 across the 21 of their papers we have counts for
7 papers · 1 filter
On instability of Type (II) Lawson-Osserman Cones
Zhaohu Nie, Yongsheng Zhang
We obtain the instability of Type (II) Lawson-Osserman cones in Euclidean spaces, and thus provide a family of (uncountably many) unstable solutions with singularity to the Dirichl…
Toda field theories and integral curves of standard differential systems
Zhaohu Nie
This paper establishes three relations between the Toda field theory associated to a simple Lie algebra and the integral curves of the standard differential system on the correspon…
Non-Rigid Parabolic Geometries of Monge Type
Ian Anderson, Zhaohu Nie, Pawel Nurowski
In this paper we study a novel class of parabolic geometries which we call parabolic geometries of Monge type. These parabolic geometries are defined by special gradings of simple…
Secondary Chern-Euler forms and the Law of Vector Fields
Zhaohu Nie
The Law of Vector Fields is a term coined by Gottlieb for a relative Poincaré-Hopf theorem. It was first proved by Morse and expresses the Euler characteristic of a manifold with b…
Secondary Chern-Euler class for general submanifold
Zhaohu Nie
We define and study the secondary Chern-Euler class for a general submanifold of a Riemannian manifold. Using this class, we define and study index for a vector field with non-isol…
On transgression in associated bundles
Zhaohu Nie
We formulate and prove a formula for transgressing characteristic forms in general associated bundles following a method of Chern. As applications, we derive D. Johnson's explicit…