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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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Journal Article
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