Continuum mechanics of media with inner structures

We propose a geometrical approach to the mechanics of continuous media equipped with inner structures and give the basic (Navier–Stokes, mass conservation and energy conservation) equations of their motion.     

When is a Riemannian submersion homogeneous?

We study the structure of the most common type of Riemannian submersions, namely those whose fibers are given by the orbits of an isometric group action on a Riemannian manifold. Special emphasis is given to the case where the ambient space has nonnegative curvature. The first author was supported by research grant MTM2004-04794-MEC. Most of this work was done during a visit of the second author to Madrid, financed in part by funds of the aforementioned grant.     

常曲率黎曼流形中的广义旋转极小超曲面

设S~(n+1)(K_0)是具有正常数截面曲率K_0的n+1维黎曼流形,若n维紧致连通广义旋转流形V~n=V~r×p~2S~(n-r)(K)极小浸入在S~(n+1)(K_0)中,则V~n或是S~(n+1)(K_0)的全测地超曲面S~n(K_0)或是V~r是S~(n+1)(K_0)的r_1(相似文献   

关于双曲空间形式的一个注记

本文主要证明一个具有光滑边界的紧黎曼流形,如果有非平凡解,则就等度量同构与双曲空间形式 会的紧区域,这里Ｄ～２■是■的Ｈｅｓｓｉａｎ与ｇ是Ｍ上的黎曼度量． 还证明关于上述方程的边值问题,只有混合边值问题,而且当ｃ＜－１时有解．     

Canonical Lorentzian spin structure and twistor spinors on the Fefferman space of a contact Riemannian manifold

The Fefferman space of a contact Riemannian manifold carries a Lorentzian spin structure canonically. On the Lorentzian spin manifold, we investigate the Dirac operator and the twistor operator closely. In particular, we show that, if the contact Riemannian manifold is integrable, then there exist non-zero global solutions of the twistor equation.     

A Note on the Linearity of Real-valued Functions with Respect to Suitable Metrics

In this paper we prove that for every real-valued Morse function φ on a smooth closed manifold ℳ and every neighborhood U of its critical points a suitable Riemannian metric μ _U exists such that φ is linear outside U     

On almost hyperHermitian structures on Riemannian manifolds and tangent bundles

Some results concerning almost hyperHermitian structures are considered, using the notions of the canonical connection and the second fundamental tensor field h of a structure on a Riemannian manifold which were introduced by the second author. With the help of any metric connection on an almost Hermitian manifold M an almost hyperHermitian structure can be constructed in the defined way on the tangent bundle TM. A similar construction was considered in [6], [7]. This structure includes two basic anticommutative almost Hermitian structures for which the second fundamental tensor fields h ¹ and h ² are computed. It allows us to consider various classes of almost hyperHermitian structures on TM. In particular, there exists an infinite-dimensional set of almost hyperHermitian structures on TTM where M is any Riemannian manifold.     

黎曼流形上不变集的分形维数估计

本文利用整体Lyapunov指数给出了光滑黎曼流形上C1-映射不变集的分形维数的上界.