摘要
本文运用拟共形曲率张量研究了Riemann流形上调和P—形式与Killing P—形式的不存在性,给出了拟共形平坦流形和拟常曲率流形上不存在非零调和P—形式与Kill-lug P—形式的条件.它们分别是K Yano,Bochner,Goldberg等相应结果的有趣推广.
In this paper,we studied non-exitence of harmonic p-formsand Killing p-forms on Riemannian manifolds under quasi-conformal curvature tensor satisfying centain conditions, and gave conditions of non-exitence for non zero harmonic p-forms and killing p-forms on conformally flat manifold and quasi-constant curvatare manifold. Our results are interesting genera lization of Yano, K. [4 5], Bochner[7] and Goldberg [6].
基金
四川师范学院青年科学基金资助课题
关键词
黎曼流形
调和p-形式
曲率张量
Harmonic p-form, Killing p-form Betti number, Quasi-conformal curvature tensor, Quasi-conformally flat manifold, Quasi-constant curvature manifold.
