Non-existence of certain 3-structures

被引：5

作者：

Kashiwada, T ^{[1
]}

Cabrera, FM

Tripathi, MM

机构：

[1] Saitama Coll, Dept Informat Sci, Kazo, Saitama 3470032, Japan

[2] Univ La Laguna, Dept Fundamental Math, Tenerife, Canary Isl, Spain

[3] Univ Lucknow, Dept Math & Astron, Lucknow 226007, Uttar Pradesh, India

[4] Pohang Univ Sci & Technol, Dept Math, Pohang 790784, South Korea

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2005年 / 35卷 / 06期

关键词：

D O I：

10.1216/rmjm/1181069625

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce the notion of an epsilon-framed 3-structure. This is a general structure which includes many widely studied 3-structures (almost quaternion, almost contact, hyper f-structure, almost product, etc.). We prove the existence of Riemannian metrics compatible with such a structure. We also study particular cases of epsilon-framed 3-structures showing the non-existence of certain remarkable types of such structures. First, we prove the non-existence of P-Sasakian almost r-paracontact 3-structures. Then, we show the nonexistence of almost r-contact S-3-structures (with r > 1). Finally, we establish the non-existence of proper trans-Sasakian almost contact 3-structures. A consequence of this last result is that any b-Kenmotsu almost contact 3-structure must be hypercosymplectic.

引用

页码：1953 / 1979

页数：27