Curvature invariants, differential operators and local homogeneity

被引：37

作者：

Prufer, F ^{[1
]}

Tricerri, F ^{[1
]}

Vanhecke, L ^{[1
]}

机构：

[1] KATHOLIEKE UNIV LEUVEN,DEPT MATH,B-3001 LOUVAIN,BELGIUM

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1996年 / 348卷 / 11期

关键词：

curvature invariants; locally homogeneous spaces; Laplacian; invariant differential operators; commutativity; spaces with volume-preserving geodesic symmetries;

D O I：

10.1090/S0002-9947-96-01686-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We first prove that a Riemannian manifold (M, g) with globally constant additive Weyl invariants is locally homogeneous. Then we use this result to show that a manifold (M, g) whose Laplacian commutes with all invariant differential operators is a locally homogeneous space.

引用

页码：4643 / 4652

页数：10

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