三维流形上的近余辛$p$-球和近余辛度量双结构

Almost Cosymplectic $p$-Spheres and Almost Cosymplectic Metric Bi-Structures on Three-Manifolds

中文关键词:  近余辛圆  近余辛球  近余辛度量双结构

英文关键词:almost cosymplectic circles  almost cosymplectic spheres  almost cosymplectic metric bi-structures

中文摘要:

      本文主要研究近余辛$p$-球和近余辛度量双结构.首先给出近余辛$p$-球的性质.其次定义了近余辛度量双结构并给出其在三维流形上的相关结论.最后分析当$(1,1)$-型张量$h_1$和$h_2$满足codazzi type 和 cyclic parallel 时具有近余辛度量双结构的三维流形的性质.

英文摘要:

      The purpose of this paper is to study almost cosymplectic $p$-spheres and almost cosymplectic metric bi-structures. Firstly, we show some properties of almost cosymplectic $p$-spheres. Then we introduce the notion of almost cosymplectic metric bi-structures and give some results on three dimensional manifolds admitting almost cosymplectic metric bi-structures. Moreover, we investigate three dimensional manifolds with almost cosymplectic metric bi-structures when the $(1, 1)$-type tensor fields $h_1$ and $h_2$ are being of codazzi type and cyclic parallel.