摘要 :
In this paper, we aim to introduce and study the (locally strongly convex) equiaffine isoparametric functions on the affine space A(n+1), making the emphasis on their relation with the affine isoparametric hypersurfaces. Motivated...
展开
In this paper, we aim to introduce and study the (locally strongly convex) equiaffine isoparametric functions on the affine space A(n+1), making the emphasis on their relation with the affine isoparametric hypersurfaces. Motivated by the case in the Euclidean space En+1, we first introduce the concept of equiaffine parallel hypersurfaces in A(n+1), and then equivalently re-define the equiaffine isoparametric hypersurfaces to be ones that are among families of equiaffine parallel hypersurfaces in A(n+1) of constant affine mean curvature. As the main result, we prove that an equiaffine isoparametric hypersurface is nothing but exactly a regular level set of some equiaffine isoparametric function.
收起
摘要 :
The purpose of the present paper is to obtain Cartan's identities for affine principal curvatures of an equiaffine isoparametric hypersurface under certain conditions. The result can be applied to a pseudo-Riemannian isoparametric...
展开
The purpose of the present paper is to obtain Cartan's identities for affine principal curvatures of an equiaffine isoparametric hypersurface under certain conditions. The result can be applied to a pseudo-Riemannian isoparametric hypersurface and a Blaschke isoparametric hypersurface.
收起
摘要 :
In this paper, we investigate the locally strongly convex affine hypersurfaces with semi-parallel cubic form relative to the Levi-Civita connection of affine metric. We obtain two results on such hypersurfaces which admit at most ...
展开
In this paper, we investigate the locally strongly convex affine hypersurfaces with semi-parallel cubic form relative to the Levi-Civita connection of affine metric. We obtain two results on such hypersurfaces which admit at most one affine principal curvature of multiplicity one: (1) classify these being not affine hyperspheres; (2) classify these affine hyperspheres with constant scalar curvature. For the latter, by proving the parallelism of their cubic forms we translate the classification into that of affine hypersurfaces with parallel cubic form, which has been completed by Hu-Li-Vrancken (J Differ Geom 87:239-307, 2011).
收起
摘要 :
Discussed is affine model of internal degrees of freedom, i.e. infinitesimal affinely rigid body in a manifold. The treatment is nonrelativistic and classical. The special stress is laid on geodetic models and invariance classific...
展开
Discussed is affine model of internal degrees of freedom, i.e. infinitesimal affinely rigid body in a manifold. The treatment is nonrelativistic and classical. The special stress is laid on geodetic models and invariance classification of a priori possible kinetic energies. Geometrically this is equivalent to deriving natural Riemannian structures in the bundle of linear frames from some geometry on the base manifold (affine connection, metric). It turns out that the general structure of dynamical balance laws resembles that derived in general relativity for the pole-dipole particle. Linear momentum and (affine) spin are coupled to the torsion and curvature tensors.
收起
原文获取