Research profile

Gabjin Yun

Works on boundaries & non-compact, almost & η-Ricci solitons and Ricci solitons.

NP-RC-739164

5
topics: 2
co-authors

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Boundaries & non-compact Almost & η-Ricci solitons Ricci solitons Einstein metrics Stability & uniqueness

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Seungsu Hwang
2 joint workslatest 2016
Jinseok Co
1 joint worklatest 2016

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2016

math.DGApr 24, 2016arXiv:1604.07018

Ridigity of Ricci Solitons with Weakly Harmonic Weyl Tensors

Seungsu Hwang, Gabjin Yun

In this paper, we prove rigidity results on gradient shrinking Ricci solitons with weakly harmonic Weyl curvature tensors. Let $(M^{n}, g)$ be a compact gradient shrinking Ricci soliton satisfying $Ric_{g} + D df = ρ g$ with $ρ > 0$ constant. We show that if $(M, g)$ satisfies $δ W (\cdot, \cdot, \nabla f) = 0$ , then $(M, g)$ is Einstein. Here $W$ denotes the Weyl curvature tensor. In the case of noncompact, if $M$ is complete and satisfies the same condition, then $M$ is rigid in the sense that $M$ is given by a quotient of product of an Einstein manifold with Euclidean space. These are generalizations of the previous known results in, and.

Ricci solitons Einstein metrics Stability & uniqueness Boundaries & non-compact

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math.DGApr 14, 2016v2arXiv:1604.04087

Bach-flat h-almost gradient Ricci solitons

Gabjin Yun, Jinseok Co, Seungsu Hwang

On an $n$ -dimensional complete manifold $M$ , consider an $h$ -almost gradient Ricci soliton, which is a generalization of a gradient Ricci soliton. We prove that if the manifold is Bach-flat and $d h / d u > 0$ , then the manifold $M$ is either Einstein or rigid. In particular, such a manifold has harmonic Weyl curvature. Moreover, if the dimension of $M$ is four, the metric $g$ is conformally flat.

Ricci solitons Almost & η-Ricci solitons Boundaries & non-compact

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Also on these topics

Others whose papers here share the most particular topics with these, in alphabetical order, leaving out co-authors. This is a similarity of tags, not a judgement.

V. Amarendra BabuShared topics: Almost & η-Ricci solitons, Einstein metrics, Boundaries & non-compact
Biswa Ranjan DattaShared topics: Almost & η-Ricci solitons, Einstein metrics, Ricci solitons
Jungwoo MoonShared topics: Almost & η-Ricci solitons, Einstein metrics, Ricci solitons
Absos Ali ShaikhShared topics: Almost & η-Ricci solitons, Einstein metrics, Boundaries & non-compact
Fengyuan ZhangShared topics: Almost & η-Ricci solitons, Einstein metrics, Boundaries & non-compact

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NP-RC-739164 is Gabjin Yun's permanent number in the Ricci flow community on Neckpinch. It stays with them through any change of name or post. More about these numbers.

A window on one part of a person's work: papers here go back to 2016 and cover Ricci flow and its neighbouring flows, with the older work the site recommends, so this page is no measure of anyone's whole output. Being listed is not an endorsement by or of the person. If two people share this name, their work may appear together here. How it is put together.