Overview and Comparative Analysis of the Properties of the Hodge-De Rham and Tachibana Operators

被引：0
|
作者：
Stepanov, S. E. [1 ]
Tsyganok, I. I. [1 ]
Mikes, J. [2 ]
机构：
[1] Finance Univ, Dept Math, Leningradsky Prospect 49-55, Moscow 125468, Russia
[2] Palacky Univ, Dept Algebra & Geometry, Olomouc 77146, Czech Republic
来源：
FILOMAT | 2015年 / 29卷 / 10期
关键词：
Riemannian manifold; second order elliptic differential operator on forms; eigenvalues; eigenforms; BETTI; FORMS; CURVATURE;
D O I：
10.2298/FIL1510429S
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the present paper we consider two natural, elliptic, self-adjoint second order differential operators acting on exterior differential forms on Riemannian manifolds. These operators are the well-known Hodge-de Rham and little-known Tachibana operators. Basic properties of these operators are very similar, or vice versa are dual with respect to each other. We review the results (partly obtained by the authors) on the geometry of these operators and demonstrate the comparative analysis of their properties.
引用
收藏
页码：2429 / 2436
页数：8
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