This article is cited in 20 papers

A New Strong Laplacian on Differential Forms

S. E. Stepanov

Vladimir State Pedagogical University

Abstract: We construct a strong Laplacian $D^*D$ by using the third operator in the basis $\{d,d^*,D\}$ of the space of natural first-order operators acting on the differential forms of a Riemannian manifold $(M,g)$. We study the properties of the Laplacian $D^*D$ and obtain Weitzenbock's formula relating the three strong Laplacians $dd^*$, $d^*d$, and $D^*D$ to the curvature of the manifold $(M,g)$.

UDC: 514.76

Received: 16.03.2000
Revised: 25.03.2004

DOI: 10.4213/mzm121

 English version: Mathematical Notes, 2004, 76:3, 420–425

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