关于共形紧致流形的一个注记

陶永芊; 彭晓芸

doi:10.3969/j.issn.1001-4926.2018.04.005

陶永芊, 彭晓芸. 关于共形紧致流形的一个注记[J]. 南昌航空大学学报(自然科学版), 2018, 32(4): 32-36. DOI: 10.3969/j.issn.1001-4926.2018.04.005

引用本文:

陶永芊, 彭晓芸. 关于共形紧致流形的一个注记[J]. 南昌航空大学学报(自然科学版), 2018, 32(4): 32-36. DOI: 10.3969/j.issn.1001-4926.2018.04.005

TAO Yong-qian, PENG Xiao-yun. A Remark on Conformally Compact Manifolds[J]. Journal of nanchang hangkong university(Natural science edition), 2018, 32(4): 32-36. DOI: 10.3969/j.issn.1001-4926.2018.04.005

Citation:

TAO Yong-qian, PENG Xiao-yun. A Remark on Conformally Compact Manifolds[J]. Journal of nanchang hangkong university(Natural science edition), 2018, 32(4): 32-36. DOI: 10.3969/j.issn.1001-4926.2018.04.005

关于共形紧致流形的一个注记

A Remark on Conformally Compact Manifolds

摘要

摘要: 对由一个分裂定理确定的共形紧致流形的结构，给出了一个注记，并且证明：若（M，g）是一个n维共形紧致流形且Ric_M≥-（n-1）和λ₀（M）=n-2，则在H¹（L²（M））中不存在任何一个k≥2正交调和形式组。

Abstract: Give a remark on conformally compact manifolds with the structure be given by an splitting type theorem and show that there are no k ≥ 2 orthogonal harmonic forms in H¹(L²(M)) under the assumption of (M,g)is an n-dimensional conformally compact manifold with Ric_M ≥ -(n-1) and λ₀(M)=n-2.

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