Some differential operators in the symmetric bundle

Kimaczyńska, Anna

doi:10.17512/jamcm.2017.3.03

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“…On the other hand, we were the first and only who began to study the properties of this operator in details (see [3,31,33,39,41,42,44]). To these lists, we can add two papers [24] and [25] in which there are terms "Sampson Laplacian" and "Sampson operator" but there are no new results on the geometry of the Sampson operator.…”

Section: Introductionmentioning

confidence: 99%

On the Sampson Laplacian

Степанов

Tsyganok

Mikeš

2019

Filomat

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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 Weitzenböck decomposition. Further we estimate operator's lowest eigenvalue.

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