Special bases for derivations of tensor algebras. I. Cases in a neighborhood and at a point

Normal frames and the validity of the equivalence principle. I. Cases in a neighborhood and at a point

A treatment in a neighborhood and at a point of the equivalence principle on the basis of derivations of the tensor algebra over a manifold is given. Necessary and sufficient conditions are given for the existence of local bases, called normal frames, in which the components of derivations vanish in a neighborhood or at a point. These frames (bases), if any, are explicitly described and the problem of their holonomicity is considered. In particular, the obtained results concern symmetric as well as nonsymmetric linear connections.

关于实代数簇管状邻域的体积

On the volume of tubular neighborhoods of real algebraic varieties

本文针对任意余维的实代数簇，推导了随机点落在其给定距离内的概率上界，该界由定义多项式的次数给出，并包含了Ocneanu的一个未发表结果。