In this paper,the invariant geometric flows for hypersurfaces in centro-affine geometry are explored.We first present evolution equations of the centro-affine invariants corresponding to the geometric flows.Based on t...In this paper,the invariant geometric flows for hypersurfaces in centro-affine geometry are explored.We first present evolution equations of the centro-affine invariants corresponding to the geometric flows.Based on these fundamental evolution equations,we show that the centro-affine heat flow for hypersurfaces is equivalent to a system of ordinary differential equations,which can be solved explicitly.Finally,the centro-affine invariant normal flows for hypersurfaces are investigated,and two specific flows are provided to illustrate the behaviour of the flows.展开更多
Group-invariant solutions to certain plane curve motions in Euclidean and centro-affine geometries areobtained. The behavior of some solutions is also presented.
基金This work was supported by National Natural Science Foundation of China(Grant Nos.11631007 and 11971251).
文摘In this paper,the invariant geometric flows for hypersurfaces in centro-affine geometry are explored.We first present evolution equations of the centro-affine invariants corresponding to the geometric flows.Based on these fundamental evolution equations,we show that the centro-affine heat flow for hypersurfaces is equivalent to a system of ordinary differential equations,which can be solved explicitly.Finally,the centro-affine invariant normal flows for hypersurfaces are investigated,and two specific flows are provided to illustrate the behaviour of the flows.
文摘Group-invariant solutions to certain plane curve motions in Euclidean and centro-affine geometries areobtained. The behavior of some solutions is also presented.
