On the Sampson Laplacian | Zendy

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

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On the Sampson Laplacian

Author(s) -

С. Е. Степанов,

Irina Tsyganok,

Josef Mikeš

Publication year - 2019

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/fil1904059s

Subject(s) - mathematics , semi elliptic operator , laplace operator , laplace–beltrami operator , p laplacian , operator (biology) , differential operator , quasinormal operator , elliptic operator , covariant transformation , pure mathematics , finite rank operator , mathematical analysis , eigenvalues and eigenvectors , mathematical physics , boundary value problem , biochemistry , chemistry , physics , repressor , quantum mechanics , transcription factor , banach space , gene

In the present paper we consider the little-known Sampson operator that is strongly elliptic and self-adjoint second order differential operator acting on covariant symmetric tensors on Riemannian manifolds. First of all, we review the results on this operator. Then we consider the properties of the Sampson operator acting on one-forms and symmetric two-tensors. We study this operator using the analytical method, due to Bochner, of proving vanishing theorems for the null space of a Laplace operator admitting a Weitzenb?ck decomposition. Further we estimate operator?s lowest eigenvalue.

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