Overview and comparative analysis of the properties of the Hodge-de Rham and Tachibana operators | Zendy

С. Е. Степанов | Zendy; Irina Tsyganok | Zendy; Josef Mikeš | Zendy

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Overview and comparative analysis of the properties of the Hodge-de Rham and Tachibana operators

Author(s) -

С. Е. Степанов,

Irina Tsyganok,

Josef Mikeš

Publication year - 2015

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1510429s

Subject(s) - mathematics , hodge theory , pure mathematics , differential operator , operator theory , order (exchange) , elliptic operator , hodge dual , algebra over a field , mathematical analysis , cohomology , finance , economics

In the present paper we consider two natural, elliptic, self-adjoint second order di erential operators acting on exterior di erential 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.

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