Almost η-Ricci solitons in (LCS)ₙ-manifolds

Adara M. Blaga

Paper · Jul 28, 2017

Almost $η$ -Ricci solitons in $(L C S)_{n}$ -manifolds

Adara M. Blaga

math.DGarXiv:1707.09343v5

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Abstract

We consider almost $η$ -Ricci solitons in $(L C S)_{n}$ -manifolds satisfying certain curvature conditions. We provide a lower and an upper bound for the norm of the Ricci curvature in the gradient case, derive a Bochner-type formula for an almost $η$ -Ricci soliton and state some consequences of it on an $(L C S)_{n}$ -manifold.

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Submitted: Jul 28, 2017
Last revised: Aug 23, 2020 (v5)
Subjects: math.DG
Journal: Bulletin of the Belgian Mathematical Society - Simon Stevin 25(5), 641-653 (2018)
DOI: 10.36045/bbms/1547780426

Comments: 15 pages

Ricci solitons Almost & η-Ricci solitons

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Ricci solitons Metrics that change under Ricci flow only by scaling and diffeomorphisms: shrinking, steady or expanding solitons. Start with: The Ricci flow on surfaces (Hamilton, 1988) Almost & η-Ricci solitons Variations on the Ricci soliton equation: let the constant λ become a function (almost solitons), add a term along a contact form (η-Ricci… Start with: Ricci almost solitons (Pigola et al., 2010)

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11B.1
Ricci SolitonsBook 11B · Solitons, Compactness and Singularities
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.
12B.2
The Asymptotic Soliton and Three-Dimensional ShrinkersBook 12B · κ-Solutions and Surgery
Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.

[1] 11B.1
Ricci SolitonsBook 11B · Solitons, Compactness and Singularities
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.

[2] 12B.2
The Asymptotic Soliton and Three-Dimensional ShrinkersBook 12B · κ-Solutions and Surgery
Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.

Almost $η$ -Ricci solitons in $(L C S)_{n}$ -manifolds

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Almost η-Ricci solitons in (LCS)n​-manifolds

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Almost $η$ -Ricci solitons in $(L C S)_{n}$ -manifolds