Rigidity Results for Riemann and Schouten Solitons

Tokura, Willian Isáo; Barboza, Marcelo; Batista, Elismar Dias; Menezes, Ilton

doi:10.1007/s00009-023-02319-z

Cited by 5 publications

(1 citation statement)

References 13 publications

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“…In the latter case, compact Riemann solitons with constant-length potential were shown to be trivial. This result was extended by Tokura, Barboza, Batista, and Menezes in [11] without additional conditions on the potential.…”

Section: Introductionsupporting

confidence: 55%

Almost Riemann Solitons with Vertical Potential on Conformal Cosymplectic Contact Complex Riemannian Manifolds

Manev

2022

Symmetry

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Almost-Riemann solitons are introduced and studied on an almost contact complex Riemannian manifold, i.e., an almost-contact B-metric manifold, which is obtained from a cosymplectic manifold of the considered type by means of a contact conformal transformation of the Reeb vector field, its dual contact 1-form, the B-metric, and its associated B-metric. The potential of the studied soliton is assumed to be in the vertical distribution, i.e., it is collinear to the Reeb vector field. In this way, manifolds from the four main classes of the studied manifolds are obtained. The curvature properties of the resulting manifolds are derived. An explicit example of dimension five is constructed. The Bochner curvature tensor is used (for a dimension of at least seven) as a conformal invariant to obtain these properties and to construct an explicit example in relation to the obtained results.

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Section: Introductionsupporting

confidence: 55%