2019
DOI: 10.3906/mat-1902-38
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Ricci–Yamabe maps for Riemannian flows and their volume variation and volume entropy

Abstract: The aim of this short note is to produce new examples of geometrical flows associated to a given Riemannian flow g(t). The considered flow in covariant symmetric 2-tensor fields will be called Ricci-Yamabe map since it involves a scalar combination of Ricci tensor and scalar curvature of g(t). Due to the signs of considered scalars the Ricci-Yamabe flow can be also a Riemannian or semi-Riemannian or singular Riemannian flow. We study the associated function of volume variation as well as the volume entropy. Fi… Show more

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Cited by 66 publications
(58 citation statements)
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“…In 2019, S. Güler et al [21] introduced a new geometry flow, which is a scalar combination of the Ricci and Yamabe flow under the Ricci-Yamabe map. The new flow is also known as the Ricci-Yamabe flow for type (ρ, q).…”
Section: Background and Motivationsmentioning
confidence: 99%
See 3 more Smart Citations
“…In 2019, S. Güler et al [21] introduced a new geometry flow, which is a scalar combination of the Ricci and Yamabe flow under the Ricci-Yamabe map. The new flow is also known as the Ricci-Yamabe flow for type (ρ, q).…”
Section: Background and Motivationsmentioning
confidence: 99%
“…Suppose that M is a Riemannian manifold of dimension n and T s 2 (M) is a linear space of its symmetric tensor fields for (0, 2)-type and Riem(M) T s 2 (M) is infinite space of its Riemannian metrics. In the paper [21], the authors have stated the below definition: Definition 1. [21] Suppose that a Riemannian flow on M is a smooth map:…”
Section: Background and Motivationsmentioning
confidence: 99%
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“…Recently, Guler and Crasmareanu [10] introduced a new geometric flow which is a scalar combination of Ricci flow and Yamabe flow, and called it as Ricci-Yamabe map. The Ricci-Yamabe flow of type (α, β) is defined as follows:…”
Section: Introductionmentioning
confidence: 99%