Noncommutative potential theory and the sign of the curvature operator in Riemannian geometry

被引：5

作者：

Cipriani, F

Sauvageot, JL

机构：

[1] Politecn Milan, Dipartimento Matemat, I-20133 Milan, Italy

[2] Univ Paris 06, CNRS, Math Inst, F-75252 Paris 05, France

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 2003年 / 13卷 / 03期

关键词：

D O I：

10.1007/s00039-003-0421-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this work is to show that in any complete Riemannian manifold M, without boundary, the curvature operator is nonnegative if and only if the Dirac Laplacian D-2 generates a C*-Markovian semigroup (i.e. a strongly continuous, completely positive, contraction semigroup) on the Clifford C*-algebra of M or, equivalently, if and only if the quadratic form epsilon(D) of D-2 is a C*-Dirichlet form.

引用

页码：521 / 545

页数：25

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