Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2017, Volume 447, Issue 2, pp. 882 - 889

Let and be two Riemannian manifolds, and a smooth map. By definition, a gradient Ricci-Harmonic soliton satisfies for some and constants and . Here is the...

Ricci-Harmonic flow | Ricci-Harmonic soliton | Ricci soliton | MATHEMATICS | MATHEMATICS, APPLIED | LOWER BOUNDS | GRADIENT SOLITONS | FLOW

Ricci-Harmonic flow | Ricci-Harmonic soliton | Ricci soliton | MATHEMATICS | MATHEMATICS, APPLIED | LOWER BOUNDS | GRADIENT SOLITONS | FLOW

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 10/2011, Volume 269, Issue 1, pp. 461 - 466

We show that a compact Ricci soliton is rigid if and only if the Weyl conformal tensor is harmonic. In the complete noncompact case we prove the same result...

Mathematics, general | Mathematics | Gradient Ricci soliton | 53C25 | Rigid Ricci soliton | Harmonic Weyl tensor | MATHEMATICS | Universities and colleges

Mathematics, general | Mathematics | Gradient Ricci soliton | 53C25 | Rigid Ricci soliton | Harmonic Weyl tensor | MATHEMATICS | Universities and colleges

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2018, Volume 465, Issue 2, pp. 1112 - 1133

We completely determine the solutions to the Ricci soliton equation among homogeneous Gödel-type metrics. Investigating the properties of these solutions, we...

Gödel-type metrics | Ricci solitons | Gradient Ricci solitons | MATHEMATICS | MATHEMATICS, APPLIED | TIMES | METRICS | COLLINEATIONS | Godel-type metrics

Gödel-type metrics | Ricci solitons | Gradient Ricci solitons | MATHEMATICS | MATHEMATICS, APPLIED | TIMES | METRICS | COLLINEATIONS | Godel-type metrics

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 03/2019, Volume 137, pp. 212 - 216

The purpose of this paper is to investigate some equations of structure for -almost Ricci soliton which are a natural generalization for almost Ricci solitons....

[formula omitted]-almost Ricci soliton | Gradient [formula omitted]-almost Ricci soliton | Hodge–de Rham decomposition | Gradient h-almost Ricci soliton | h-almost Ricci soliton | MATHEMATICS | COMPACT | Hodge-de Rham decomposition | PHYSICS, MATHEMATICAL

[formula omitted]-almost Ricci soliton | Gradient [formula omitted]-almost Ricci soliton | Hodge–de Rham decomposition | Gradient h-almost Ricci soliton | h-almost Ricci soliton | MATHEMATICS | COMPACT | Hodge-de Rham decomposition | PHYSICS, MATHEMATICAL

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 04/2017, Volume 114, pp. 216 - 222

We introduce the concept which extends naturally the by Pigola–Rigoli–Rimoldi–Setti and show that a compact nontrivial -almost Ricci soliton of dimension no...

Scalar curvature | [formula omitted]-almost Ricci soliton | [formula omitted]-quasi-Einstein metric | COMPACT | MATHEMATICS, APPLIED | m-quasi-Einstein metric | CONSTANT SCALAR CURVATURE | h-almost Ricci soliton | PHYSICS, MATHEMATICAL | GRADIENT | COMPLETE RIEMANNIAN-MANIFOLDS

Scalar curvature | [formula omitted]-almost Ricci soliton | [formula omitted]-quasi-Einstein metric | COMPACT | MATHEMATICS, APPLIED | m-quasi-Einstein metric | CONSTANT SCALAR CURVATURE | h-almost Ricci soliton | PHYSICS, MATHEMATICAL | GRADIENT | COMPLETE RIEMANNIAN-MANIFOLDS

Journal Article

Journal of Geometry, ISSN 0047-2468, 12/2017, Volume 108, Issue 3, pp. 1031 - 1037

We obtain an intrinsic formula of a Ricci soliton vector field and a differential condition for the non-steady case to be gradient. Next we provide a condition...

Geometry | Ricci soliton | Gradient | Harmonic form | 53C55 | 53C44 | 53C21 | Kaehler–Ricci soliton | Mathematics | Intrinsic formula

Geometry | Ricci soliton | Gradient | Harmonic form | 53C55 | 53C44 | 53C21 | Kaehler–Ricci soliton | Mathematics | Intrinsic formula

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 2018, Volume 293, Issue 1, pp. 75 - 99

We construct examples of Bach-flat gradient Ricci solitons in neutral signature which are neither half conformally flat nor conformally Einstein.

Bach tensor | Riemannian extension | Gradient Ricci soliton | Affine surface | MATHEMATICS | SPACES | gradient Ricci soliton | affine surface | EINSTEIN MANIFOLDS | Mathematics - Differential Geometry

Bach tensor | Riemannian extension | Gradient Ricci soliton | Affine surface | MATHEMATICS | SPACES | gradient Ricci soliton | affine surface | EINSTEIN MANIFOLDS | Mathematics - Differential Geometry

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 12/2019, Volume 69, Issue 6, pp. 1447 - 1458

In this paper, we consider *-Ricci soliton in the frame-work of Kenmotsu manifolds. First, we prove that if ( , ) is a Kenmotsu manifold and is a *-Ricci...

Ricci soliton | 53C44 | 53D10 | 53D15 | Kenmotsu manifold | gradient almost -Ricci soliton | Primary 53C25 | Einstein manifold | Mathematics - Differential Geometry

Ricci soliton | 53C44 | 53D10 | 53D15 | Kenmotsu manifold | gradient almost -Ricci soliton | Primary 53C25 | Einstein manifold | Mathematics - Differential Geometry

Journal Article

Publicationes Mathematicae, ISSN 0033-3883, 2018, Volume 93, Issue 1-2, pp. 241 - 252

In the present paper, we study *-Ricci solitons and prove that if a Sasakian 3-manifold M admits *-Ricci soliton, then it has constant scalar curvature, and...

Einstein | gradient Ricci solitons | Ricci solitons | MATHEMATICS | VECTOR-FIELDS | QUASI-EINSTEIN METRICS

Einstein | gradient Ricci solitons | Ricci solitons | MATHEMATICS | VECTOR-FIELDS | QUASI-EINSTEIN METRICS

Journal Article

Colloquium Mathematicum, ISSN 0010-1354, 07/2015, Volume 141, Issue 1, pp. 125 - 141

For complete gradient Ricci solitons we state necessary conditions for a non-trivial soliton structure in terms of intrinsic curvature invariants.

Intrinsic curvature | Complete gradient Ricci soliton | Maximum principle of Omori-Yau | MATHEMATICS | maximum principle of Omori-Yau | complete gradient Ricci soliton | intrinsic curvature | COMPLETE RIEMANNIAN MANIFOLDS

Intrinsic curvature | Complete gradient Ricci soliton | Maximum principle of Omori-Yau | MATHEMATICS | maximum principle of Omori-Yau | complete gradient Ricci soliton | intrinsic curvature | COMPLETE RIEMANNIAN MANIFOLDS

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 2017, Volume 288, Issue 2, pp. 475 - 488

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...

Einstein metric | h-almost gradient Ricci soliton | Bach-flat | MATHEMATICS | Mathematics - Differential Geometry

Einstein metric | h-almost gradient Ricci soliton | Bach-flat | MATHEMATICS | Mathematics - Differential Geometry

Journal Article

PACIFIC JOURNAL OF MATHEMATICS, ISSN 0030-8730, 07/2019, Volume 301, Issue 1, pp. 371 - 384

In this paper, we prove some classification theorems for gradient expanding and steady Ricci solitons. We show that a complete noncompact radially Ricci flat...

MATHEMATICS | gradient expanding Ricci soliton | ROTATIONAL SYMMETRY | gradient steady Ricci soliton

MATHEMATICS | gradient expanding Ricci soliton | ROTATIONAL SYMMETRY | gradient steady Ricci soliton

Journal Article

Publicationes Mathematicae, ISSN 0033-3883, 2017, Volume 91, Issue 3-4, pp. 309 - 319

In this work, we study warped Finslerian gradient Ricci solitons where the base space is Riemannian, and it is showed that the potential function depends only...

Finsler space | Warped product | Gradient Ricci soliton | MATHEMATICS | SPACES | warped product | CURVATURE | gradient Ricci soliton | MANIFOLDS

Finsler space | Warped product | Gradient Ricci soliton | MATHEMATICS | SPACES | warped product | CURVATURE | gradient Ricci soliton | MANIFOLDS

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2018, Volume 146, Issue 1, pp. 359 - 368

In this short note, using Günther's volume comparison theorem and Yokota's gap theorem on complete shrinking gradient Ricci solitons, we prove that for any...

Shrinking gradient Ricci solitons | Gap theorem | Sectional curvature | MATHEMATICS | MATHEMATICS, APPLIED | CURVATURE | PERELMANS REDUCED VOLUME | gap theorem | FLOW | sectional curvature

Shrinking gradient Ricci solitons | Gap theorem | Sectional curvature | MATHEMATICS | MATHEMATICS, APPLIED | CURVATURE | PERELMANS REDUCED VOLUME | gap theorem | FLOW | sectional curvature

Journal Article

FILOMAT, ISSN 0354-5180, 2018, Volume 32, Issue 13, pp. 4679 - 4687

The object of the present paper is to study Ricci solitons on eta-Einstein contact manifolds. As a consequence of the main result we deduce some important...

MATHEMATICS | recurrent manifolds | COMPACT | MATHEMATICS, APPLIED | GRADIENT RICCI | eta-Einstein manifold | homothetic vector field | METRICS | Ricci solitons | contact manifolds | Einstein manifold

MATHEMATICS | recurrent manifolds | COMPACT | MATHEMATICS, APPLIED | GRADIENT RICCI | eta-Einstein manifold | homothetic vector field | METRICS | Ricci solitons | contact manifolds | Einstein manifold

Journal Article

FILOMAT, ISSN 0354-5180, 2017, Volume 31, Issue 18, pp. 5791 - 5801

If the potential vector field of an eta-Ricci soliton is of gradient type, using Bochner formula, we derive from the soliton equation a nonlinear second order...

MATHEMATICS | MATHEMATICS, APPLIED | Laplacian equation | CURVATURE | MANIFOLDS | gradient eta-Ricci solitons | scalar curvature | GEOMETRY

MATHEMATICS | MATHEMATICS, APPLIED | Laplacian equation | CURVATURE | MANIFOLDS | gradient eta-Ricci solitons | scalar curvature | GEOMETRY

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 08/2009, Volume 137, Issue 8, pp. 2755 - 2759

A gradient Ricci soliton is a triple (M,g,f) satisfying R_{ij}+\nabla _i\nabla _j f =\lambda g_{ij} for some real number \lambda . In this paper, we will show...

Riemann manifold | Mathematical completeness | Mathematical theorems | Solitons | Vector fields | Mathematical functions | Mathematics | Curvature | Gradient self-similar solution | Completeness | Gradient Ricci soliton | MATHEMATICS | MATHEMATICS, APPLIED | gradient Ricci soliton | gradient self-similar solution

Riemann manifold | Mathematical completeness | Mathematical theorems | Solitons | Vector fields | Mathematical functions | Mathematics | Curvature | Gradient self-similar solution | Completeness | Gradient Ricci soliton | MATHEMATICS | MATHEMATICS, APPLIED | gradient Ricci soliton | gradient self-similar solution

Journal Article

Journal of Geometric Analysis, ISSN 1050-6926, 7/2013, Volume 23, Issue 3, pp. 1196 - 1212

It is shown that locally conformally flat Lorentzian gradient Ricci solitons are locally isometric to a Robertson–Walker warped product, if the gradient of the...

53C50 | 53C21 | Mathematics | 53C25 | Abstract Harmonic Analysis | Lorentzian locally conformally flat manifolds | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Ricci solitons | Gradient Ricci solitons | Differential Geometry | Dynamical Systems and Ergodic Theory | MATHEMATICS | EINSTEIN-SPACES

53C50 | 53C21 | Mathematics | 53C25 | Abstract Harmonic Analysis | Lorentzian locally conformally flat manifolds | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Ricci solitons | Gradient Ricci solitons | Differential Geometry | Dynamical Systems and Ergodic Theory | MATHEMATICS | EINSTEIN-SPACES

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 01/2020, Volume 147, p. 103535

Inspired by the Bach tensor on Riemannian manifolds, we introduce the -tensor ( ) on Kähler manifolds. We prove that a compact gradientKähler–Ricci soliton...

Extremal | [formula omitted]-tensor | Kähler–Einstein | Gradient Kähler–Ricci soliton | MATHEMATICS | PHYSICS, MATHEMATICAL | Gradient Kahler-Ricci soliton | Kahler-Einstein | B-tensor

Extremal | [formula omitted]-tensor | Kähler–Einstein | Gradient Kähler–Ricci soliton | MATHEMATICS | PHYSICS, MATHEMATICAL | Gradient Kahler-Ricci soliton | Kahler-Einstein | B-tensor

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2016, Volume 144, Issue 1, pp. 369 - 378

We use the theory of isoparametric functions to investigate gradient Ricci solitons with constant scalar curvature. We show rigidity of gradient Ricci solitons...

Gradient ricci soliton | Scalar curvature | MATHEMATICS | MATHEMATICS, APPLIED | Gradient Ricci soliton | scalar curvature

Gradient ricci soliton | Scalar curvature | MATHEMATICS | MATHEMATICS, APPLIED | Gradient Ricci soliton | scalar curvature

Journal Article

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