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Articles de revues sur le sujet « Ricci »

Auteur : Grafiati

Publié le 4 juin 2021

Mis à jour le 26 juillet 2025

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1

Stepanov, S. E., I. I. Tsyganok, and J. Mikeš. "Complete Riemannian manifolds with Killing — Ricci and Codazzi — Ricci tensors." Differential Geometry of Manifolds of Figures, no. 53 (2022): 112–17. http://dx.doi.org/10.5922/0321-4796-2022-53-10.

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The purpose of this paper is to prove of Liouville type theorems, i. e., theorems on the non-existence of Killing — Ricci and Codazzi — Ricci tensors on complete non-compact Riemannian manifolds. Our results complement the two classical vanishing theorems from the last chapter of famous Besse’s monograph on Einstein manifolds.

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2

Aytpanova, Aray Amangeldiyevna. "RICCI CURVATURE AND THE RICCI OPERATOR." Theoretical & Applied Science 1, no. 05 (2013): 12–17. http://dx.doi.org/10.15863/tas.2013.05.1.3.

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3

Majhi, Pradip, Uday Chand De та Debabrata Kar. "η-Ricci Solitons on Sasakian 3-Manifolds". Annals of West University of Timisoara - Mathematics and Computer Science 55, № 2 (2017): 143–56. http://dx.doi.org/10.1515/awutm-2017-0019.

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AbstractIn this paper we studyη-Ricci solitons on Sasakian 3-manifolds. Among others we prove that anη-Ricci soliton on a Sasakian 3-manifold is anη-Einstien manifold. Moreover we considerη-Ricci solitons on Sasakian 3-manifolds with Ricci tensor of Codazzi type and cyclic parallel Ricci tensor. Beside these we study conformally flat andφ-Ricci symmetricη-Ricci soliton on Sasakian 3-manifolds. Alsoη-Ricci soliton on Sasakian 3-manifolds with the curvature conditionQ.R= 0 have been considered. Finally, we construct an example to prove the non-existence of properη-Ricci solitons on Sasakian 3-ma

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4

De, Uday Chand, and Krishanu Mandal. "Ricci Solitons and Gradient Ricci Solitons on N(k)-Paracontact Manifolds." Zurnal matematiceskoj fiziki, analiza, geometrii 15, no. 3 (2019): 307–20. http://dx.doi.org/10.15407/mag15.03.307.

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5

Uygun, Pakize, Mehmet Atçeken та Tugba Mert. "Ricci-pseudosymmetric almost α -cosymplectic ( k , μ , ν ) -spaces admitting Ricci solitons". Ukrains’kyi Matematychnyi Zhurnal 77, № 1 (2025): 78. https://doi.org/10.3842/umzh.v77i1.7922.

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UDC 514.7 We study some types of Ricci pseudosymmetric α -cosymplectic ( k , μ , ν ) -spaces whose metric admits Ricci solitons. We present some results obtained for Ricci solitons on Ricci pseudosymmetric, projective Ricci pseudosymmetric, concircular Ricci pseudosymmetric, and W 1 -Ricci pseudosymmetric spaces. Some results on almost α -cosymplectic ( k , μ , ν ) -spaces are also presented. Finally, we give an example for the 5-dimensional case.

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6

Almia, Priyanka, та Jaya Upreti. "Certain properties of η-Ricci soliton on η-Einstein para-Kenmotsu manifolds". Filomat 37, № 28 (2023): 9575–85. http://dx.doi.org/10.2298/fil2328575a.

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The objective of present research paper is to be investigate the geometric properties of ?-Ricci solitons on ?-Einstein para-Kenmotsu manifolds. In this manner, we consider ?-Ricci solitons on ?-Einstein para-Kenmotsu manifolds satistfying R.S = 0. Further, we obtain results for ?-Ricci solitons on ?-Einstein para-Kenmotsu manifolds with quasi-conformal flat property. Moreover, we get result for ?-Ricci solitins in ?-Einstein para-Kenmotsu manifolds admitting Codazzi type of Ricci tensor and cyclic parallel Ricci tensor, ?-quasi-conformally semi-symmetric, ?-Ricci symmetric and quasi-conformal

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7

Lai, Yi. "Producing 3D Ricci flows with nonnegative Ricci curvature via singular Ricci flows." Geometry & Topology 25, no. 7 (2021): 3629–90. http://dx.doi.org/10.2140/gt.2021.25.3629.

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8

ZHANG, ZHOU. "RICCI LOWER BOUND FOR KÄHLER–RICCI FLOW." Communications in Contemporary Mathematics 16, no. 02 (2014): 1350053. http://dx.doi.org/10.1142/s0219199713500533.

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We provide general discussion on the lower bound of Ricci curvature along Kähler–Ricci flows over closed manifolds. The main result is the non-existence of Ricci lower bound for flows with finite time singularities and non-collapsed global volume. As an application, we give examples showing that positivity of Ricci curvature would not be preserved by Ricci flow in general.

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9

Kim, Byung, Jin Choi, and Sang Lee. "On almost generalized gradient Ricci-Yamabe soliton." Filomat 38, no. 11 (2024): 3825–37. https://doi.org/10.2298/fil2411825k.

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Inthis paper, we study the geometric characterizations and classify of the Riemannian manifold with generalized gradient Ricci-Yamabe soliton or almost generalized gradient Ricci-Yamabe soliton. In addition, theorems were obtained to construct a model space with gradient Ricci-Yamabe soliton, general-ized gradient Ricci-Yamabe soliton, almost gradient Ricci-Yamabe soliton and almost generalized gradient Ricci-Yamabe soliton.

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10

De, Krishnendu, та Uday Chand De. "η-Ricci Solitons on Kenmotsu 3-Manifolds". Annals of West University of Timisoara - Mathematics and Computer Science 56, № 1 (2018): 51–63. http://dx.doi.org/10.2478/awutm-2018-0004.

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Abstract In the present paper we study η-Ricci solitons on Kenmotsu 3-manifolds. Moreover, we consider η-Ricci solitons on Kenmotsu 3-manifolds with Codazzi type of Ricci tensor and cyclic parallel Ricci tensor. Beside these, we study φ-Ricci symmetric η-Ricci soliton on Kenmotsu 3-manifolds. Also Kenmotsu 3-manifolds satisfying the curvature condition R.R = Q(S, R)is considered. Finally, an example is constructed to prove the existence of a proper η-Ricci soliton on a Kenmotsu 3-manifold.

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11

Tang, Wanxiao, Jon Yong, Ho Yun, Guoqing He, and Peibiao Zhao. "Geometries of manifolds equipped with a Ricci (projection-Ricci) quarter-symmetric connection." Filomat 33, no. 16 (2019): 5237–48. http://dx.doi.org/10.2298/fil1916237t.

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We first introduce a Ricci quarter-symmetric connection and a projective Ricci quarter-symmetric connection, and then we investigate a Riemannian manifold admitting a Ricci (projective Ricci) quartersymmetric connection (M,g), and prove that a Riamannian manifold with a Ricci(projection-Ricci) quartersymmetric connection is of a constant curvature manifold. Furthermore, wederive that an Einstein manifold (M,g) is conformally flat under certain condition.

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12

Mert, Tuğba. "On a Classification of Almost C α -Manifolds". Journal of Mathematics 2022 (20 червня 2022): 1–11. http://dx.doi.org/10.1155/2022/5173330.

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In this paper, pseudosymmetric and Ricci pseudosymmetric almost C α -manifold are studied. For an almost C α -manifold, Riemann pseudosymmetric, Riemann Ricci pseudosymmetric, Ricci pseudosymmetric, projective pseudosymmetric, projective Ricci pseudosymmetric, concircular pseudosymmetric, and concircular Ricci pseudosymmetric cases are considered and new results are obtained.

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13

Sarkar, Sumanjit, Santu Dey, and Xiaomin Chen. "Certain results of conformal and *-conformal Ricci soliton on para-cosymplectic and para-Kenmotsu manifolds." Filomat 35, no. 15 (2021): 5001–15. http://dx.doi.org/10.2298/fil2115001s.

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The goal of the paper is to deliberate conformal Ricci soliton and *-conformal Ricci soliton within the framework of paracontact geometry. Here we prove that if an ?-Einstein para-Kenmotsu manifold admits conformal Ricci soliton and *-conformal Ricci soliton, then it is Einstein. Further we have shown that 3-dimensional para-cosymplectic manifold is Ricci flat if the manifold satisfies conformal Ricci soliton where the soliton vector field is conformal. We have also constructed some examples of para-Kenmotsu manifold that admits conformal and *-conformal Ricci soliton and verify our results.

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14

Ma, Li. "Expanding Ricci solitons with pinched Ricci curvature." Kodai Mathematical Journal 34, no. 1 (2011): 140–43. http://dx.doi.org/10.2996/kmj/1301576768.

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15

Maschler, Gideon. "Special Kähler–Ricci potentials and Ricci solitons." Annals of Global Analysis and Geometry 34, no. 4 (2008): 367–80. http://dx.doi.org/10.1007/s10455-008-9114-z.

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16

Yadav, S., and D. L. Suthar. "On Kenmatsu manifolds Satisfying Certain Conditions." Journal of the Tensor Society 3, no. 00 (2009): 19–26. http://dx.doi.org/10.56424/jts.v3i01.9968.

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In this paper, we study 3-dimensional Kenmostu manifolds, weakely Ricci symmetric Kenmostu manifolds and generalized Ricci recurrent Kenmostu manifolds and prove that conformably flat Kenmostu manifold is -Einstein manifolds, deduced that the square length of Ricci tensor. Further proved that if weakly Ricci-symmetric Kenmostu manifolds satisfies Ricci symmetric condition then manifolds Einstein manifold. In last we prove that if generalized Ricci recurrent Kenmostu manifolds satisfies the condition ( )(Y)=0 then .

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17

Yadav, S., and D. L. Suthar. "On Kenmatsu manifolds Satisfying Certain Conditions." Journal of the Tensor Society 3, no. 01 (2009): 19–26. http://dx.doi.org/10.56424/jts.v3i00.9968.

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In this paper, we study 3-dimensional Kenmostu manifolds, weakely Ricci symmetric Kenmostu manifolds and generalized Ricci recurrent Kenmostu manifolds and prove that conformably flat Kenmostu manifold is -Einstein manifolds, deduced that the square length of Ricci tensor. Further proved that if weakly Ricci-symmetric Kenmostu manifolds satisfies Ricci symmetric condition then manifolds Einstein manifold. In last we prove that if generalized Ricci recurrent Kenmostu manifolds satisfies the condition ( )(Y)=0 then .

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18

Sarkar, Avijit, та Arpan Sardar. "η-Ricci solitons on N(k)-contact metric manifolds". Filomat 35, № 11 (2021): 3879–89. http://dx.doi.org/10.2298/fil2111879s.

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In this paper, we study ?-Ricci solitons on N(k)-contact metric manifolds. At first we consider ?-Ricci solitons on N(k)-contact metric manifolds with harmonic curvature tensor. Then we study ?-Ricci solitons onN(k)-contact metric manifolds with harmonic Weyl tensor. Moreover, we consider ?-Ricci soliton on N(k)-contact metric manifolds with ?-parallel Ricci tensor. Also ?-Ricci soliton on N(k)-contact metric manifolds satisfying some curvature restrictions under projective curvature tensor have been considered. Finally, the existence of an ?-Ricci soliton on a 3-dimensional N(k)-contact metri

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19

Deshmukh, Sharief, and Hana Alsodais. "A Note on Ricci Solitons." Symmetry 12, no. 2 (2020): 289. http://dx.doi.org/10.3390/sym12020289.

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In this paper, we characterize trivial Ricci solitons. We observe the important role of the energy function f of a Ricci soliton (half the squared length of the potential vector field) in the charectrization of trivial Ricci solitons. We find three characterizations of connected trivial Ricci solitons by imposing different restrictions on the energy function. We also use Hessian of the potential function to characterize compact trivial Ricci solitons. Finally, we show that a solution of a Poisson equation is the energy function f of a compact Ricci soliton if and only if the Ricci soliton is t

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20

CAO, XIAODONG, BIAO WANG, and ZHOU ZHANG. "ON LOCALLY CONFORMALLY FLAT GRADIENT SHRINKING RICCI SOLITONS." Communications in Contemporary Mathematics 13, no. 02 (2011): 269–82. http://dx.doi.org/10.1142/s0219199711004191.

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In this paper, we first apply an integral identity on Ricci solitons to prove that closed locally conformally flat gradient Ricci solitons are of constant sectional curvature. We then generalize this integral identity to complete noncompact gradient shrinking Ricci solitons, under the conditions that the Ricci curvature is bounded from below and the Riemannian curvature tensor has at most exponential growth. As a consequence, we classify complete locally conformally flat gradient shrinking Ricci solitons with Ricci curvature bounded from below.

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21

Prasad, Rajendra, та Vinay Kumar. "Kenmotsu 3-manifold admitting gradient Ricci-Yamabe solitons and *-η-Ricci-Yamabe solitons". Filomat 38, № 13 (2024): 4569–83. https://doi.org/10.2298/fil2413569p.

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In this paper, we classify Kenmotsu manifolds admitting gradient Ricci-Yamabe solitons and *-?-Ricci-Yamabe solitons. We find conditions of Kenmotsu manifold about when it shrink, expand and steady. It is shown that Kenmotsu 3-manifold endowed with gradient Ricci-Yamabe soliton and with constant scalar curvature becomes an Einstein manifold. We, also study Kenmotsu manifold admitting *-?-Ricci-Yamabe solitons becomes generalized ?-Einstein manifold and the curvature condition R.S = 0. Finally, we provide two examples which proves existence of gradient Ricci-Yamabe soliton and *-?-Ricci-Yamabe

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22

Hussain, Ibrar, Tahirullah, and Suhail Khan. "Four-dimensional Lorentzian plane symmetric static Ricci solitons." International Journal of Modern Physics D 28, no. 16 (2019): 2040010. http://dx.doi.org/10.1142/s0218271820400106.

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Our focus is to investigate the Ricci solitons of the plane symmetric and static four-dimensional Lorentzian metrics. It is found that these metrics admit shrinking and concircular potential Ricci soliton vector fields with either 6- or 10-dimensional Lie algebra. Further, it is observed that the 4-dimensional Lorentzian static Ricci soliton manifolds are Einsteinian and hence the Ricci solitons are the trivial Ricci solitons.

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23

Bhattacharyya, Sujit, Suraj Ghosh, and Shyamal Hui. "Bernstein type gradient estimation for weighted local heat equation." Filomat 38, no. 17 (2024): 6125–34. https://doi.org/10.2298/fil2417125b.

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In this article we derive Bernstein type gradient estimation for local weighted heat equation on static weighted Riemannian manifold and evolving weighted Riemannian manifold along local Ricci flow and extended local Ricci flow. We showed that along local Ricci flow and extended local Ricci flow we can derive Bernstein type estimation for weighted heat equation without any assumption on the bound of Bakry-?mery Ricci curvature.

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24

Aquib, Md, Oğuzhan Bahadır, Laltluangkima Chawngthu, and Rajesh Kumar. "Geometric and Structural Properties of Indefinite Kenmotsu Manifolds Admitting Eta-Ricci–Bourguignon Solitons." Mathematics 13, no. 12 (2025): 1965. https://doi.org/10.3390/math13121965.

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This paper undertakes a detailed study of η-Ricci–Bourguignon solitons on ϵ-Kenmotsu manifolds, with particular focus on three special types of Ricci tensors: Codazzi-type, cyclic parallel and cyclic η-recurrent tensors that support such solitonic structures. We derive key curvature conditions satisfying Ricci semi-symmetric (R·E=0), conharmonically Ricci semi-symmetric (C(ξ,βX)·E=0), ξ-projectively flat (P(βX,βY)ξ=0), projectively Ricci semi-symmetric (L·P=0) and W5-Ricci semi-symmetric (W(ξ,βY)·E=0), respectively, with the admittance of η-Ricci–Bourguignon solitons. This work further explore

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25

Dey, Santu, та Siraj Uddin. "Characterization of almost +-conformal η-Ricci soliton on para-Kenmotsu manifolds". Filomat 37, № 11 (2023): 3601–14. https://doi.org/10.2298/fil2311601d.

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The goal of this research paper is to deliberate +-conformal ?-Ricci soliton and gradient almost +-conformal ?-Ricci soliton within the framework of para-Kenmotsu manifolds as a characterization of Einstein metrics. Here, we explore that a para-Kenmotsu metric as a +-conformal ?-Ricci soliton is Einstein metric if the soliton vector field is contact and the vector field is strictly infinitesimal contact transformation. Next, we turn up the nature of the soliton and discover the scalar curvature when the manifold admitting +-conformal ?-Ricci soliton on para-Kenmotsu manifold. After that, we ha

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26

Zhang, Pengfei, Yanlin Li, Soumendu Roy, Santu Dey, and Arindam Bhattacharyya. "Geometrical Structure in a Perfect Fluid Spacetime with Conformal Ricci–Yamabe Soliton." Symmetry 14, no. 3 (2022): 594. http://dx.doi.org/10.3390/sym14030594.

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The present paper aims to deliberate the geometric composition of a perfect fluid spacetime with torse-forming vector field ξ in connection with conformal Ricci–Yamabe metric and conformal η-Ricci–Yamabe metric. We delineate the conditions for conformal Ricci–Yamabe soliton to be expanding, steady or shrinking. We also discuss conformal Ricci–Yamabe soliton on some special types of perfect fluid spacetime such as dust fluid, dark fluid and radiation era. Furthermore, we design conformal η-Ricci–Yamabe soliton to find its characteristics in a perfect fluid spacetime and lastly acquired Laplace

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27

Singh, Jay, and Robert Sumlalsanga. "Conformal Ricci-Yamabe solitons on warped product manifolds." Filomat 38, no. 11 (2024): 3791–802. https://doi.org/10.2298/fil2411791s.

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Self-similar solutions of the conformal Ricci-Yamabe flow equation are called conformal Ricci-Yamabe solitons. This paper mainly concerned with the study of conformal Ricci-Yamabe solitons within the structure of warped product manifolds, which extend the notion of usual Riemannian product manifolds. First, the proof is provided that the base and the fiber sharing the same property implies the existence of a warped product manifold admitting a conformal Ricci-Yamabe soliton. In the next section, warped product manifolds are used to study the characterization of conformal Ricci-Yamabe solitons

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28

Meri̇ç, Şemsi̇ Eken, and Erol Kiliç. "Riemannian submersions whose total manifolds admit a Ricci soliton." International Journal of Geometric Methods in Modern Physics 16, no. 12 (2019): 1950196. http://dx.doi.org/10.1142/s0219887819501962.

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In this paper, we study Riemannian submersions whose total manifolds admit a Ricci soliton. Here, we characterize any fiber of such a submersion is Ricci soliton or almost Ricci soliton. Indeed, we obtain necessary conditions for which the target manifold of Riemannian submersion is a Ricci soliton. Moreover, we study the harmonicity of Riemannian submersion from Ricci soliton and give a characterization for such a submersion to be harmonic.

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29

Li, Benling, and Zhongmin Shen. "Ricci Curvature Tensor and Non-Riemannian Quantities." Canadian Mathematical Bulletin 58, no. 3 (2015): 530–37. http://dx.doi.org/10.4153/cmb-2014-063-4.

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AbstractThere are several notions of Ricci curvature tensor in Finsler geometry and spray geometry. One of them is defined by the Hessian of the well-known Ricci curvature. In this paper we will introduce a new notion of Ricci curvature tensor and discuss its relationship with the Ricci curvature and some non-Riemannian quantities. Using this Ricci curvature tensor, we shall have a better understanding of these non-Riemannian quantities.

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30

Ma, Rongsheng, and Donghe Pei. "$ \ast $-Ricci tensor on $ (\kappa, \mu) $-contact manifolds." AIMS Mathematics 7, no. 7 (2022): 11519–28. http://dx.doi.org/10.3934/math.2022642.

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<abstract><p>We introduce the notion of semi-symmetric $ \ast $-Ricci tensor and illustrate that a non-Sasakian $ (\kappa, \mu) $-contact manifold is $ \ast $-Ricci semi-symmetric or has parallel $ \ast $-Ricci operator if and only if it is $ \ast $-Ricci flat. Then we find that among the non-Sasakian $ (\kappa, \mu) $-contact manifolds with the same Boeckx invariant $ I_M $, only one is $ \ast $-Ricci flat, so we can think of it as the representative of such class. We also give two methods to construct $ \ast $-Ricci flat $ (\kappa, \mu) $-contact manifolds.</p></abstract

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Li, Yanlin, Dipen Ganguly, Santu Dey, and Arindam Bhattacharyya. "Conformal $ \eta $-Ricci solitons within the framework of indefinite Kenmotsu manifolds." AIMS Mathematics 7, no. 4 (2022): 5408–30. http://dx.doi.org/10.3934/math.2022300.

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<abstract><p>The present paper is to deliberate the class of $ \epsilon $-Kenmotsu manifolds which admits conformal $ \eta $-Ricci soliton. Here, we study some special types of Ricci tensor in connection with the conformal $ \eta $-Ricci soliton of $ \epsilon $-Kenmotsu manifolds. Moving further, we investigate some curvature conditions admitting conformal $ \eta $-Ricci solitons on $ \epsilon $-Kenmotsu manifolds. Next, we consider gradient conformal $ \eta $-Ricci solitons and we present a characterization of the potential function. Finally, we develop an illustrative example for

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32

SHEN, ZHONGMIN, and GUOJUN YANG. "RANDERS METRICS OF REVERSIBLE CURVATURE." International Journal of Mathematics 24, no. 01 (2013): 1350006. http://dx.doi.org/10.1142/s0129167x13500067.

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In this paper, we introduce the notions of R-reversibility and Ricci-reversibility. We prove that Randers metrics are R-reversible or Ricci-reversible if and only if they are R-quadratic or Ricci-quadratic, respectively. Besides, we discuss the properties of Ricci- or R-reversible Randers metrics which are also weakly Einsteinian, or Douglassian, or of scalar flag curvature. In particular, we determine the local structure of Randers metrics which are Ricci-reversible and locally projectively flat, and prove that an n (≥ 3)-dimensional Ricci-reversible Randers metric of non-zero scalar flag cur

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Deshmukh, Sharief, Nasser Bin Turki, and Hana Alsodais. "Characterizations of Trivial Ricci Solitons." Advances in Mathematical Physics 2020 (April 10, 2020): 1–6. http://dx.doi.org/10.1155/2020/9826570.

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Finding characterizations of trivial solitons is an important problem in geometry of Ricci solitons. In this paper, we find several characterizations of a trivial Ricci soliton. First, on a complete shrinking Ricci soliton, we show that the scalar curvature satisfying a certain inequality gives a characterization of a trivial Ricci soliton. Then, it is shown that the potential field having geodesic flow and length of potential field satisfying certain inequality gives another characterization of a trivial Ricci soliton. Finally, we show that the potential field of constant length satisfying an

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Ma, Rongsheng, and Donghe Pei. "The ∗-Ricci Operator on Hopf Real Hypersurfaces in the Complex Quadric." Mathematics 11, no. 1 (2022): 90. http://dx.doi.org/10.3390/math11010090.

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We study the ∗-Ricci operator on Hopf real hypersurfaces in the complex quadric. We prove that for Hopf real hypersurfaces in the complex quadric, the ∗-Ricci tensor is symmetric if and only if the unit normal vector field is singular. In the following, we obtain that if the ∗-Ricci tensor of Hopf real hypersurfaces in the complex quadric is symmetric, then the ∗-Ricci operator is both Reeb-flow-invariant and Reeb-parallel. As the correspondence to the semi-symmetric Ricci tensor, we give a classification of real hypersurfaces in the complex quadric with the semi-symmetric ∗-Ricci tensor.

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De, Uday Chand, Mohammad Nazrul Islam Khan, and Arpan Sardar. "h-Almost Ricci–Yamabe Solitons in Paracontact Geometry." Mathematics 10, no. 18 (2022): 3388. http://dx.doi.org/10.3390/math10183388.

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In this article, we classify h-almost Ricci–Yamabe solitons in paracontact geometry. In particular, we characterize para-Kenmotsu manifolds satisfying h-almost Ricci–Yamabe solitons and 3-dimensional para-Kenmotsu manifolds obeying h-almost gradient Ricci–Yamabe solitons. Then, we classify para-Sasakian manifolds and para-cosymplectic manifolds admitting h-almost Ricci–Yamabe solitons and h-almost gradient Ricci–Yamabe solitons, respectively. Finally, we construct an example to illustrate our result.

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36

Prasad, Rajendra, Abhinav Verma, Mohd Bilal, Abdul Haseeb, and Vindhyachal Singh Yadav. "Geometry of Certain Almost Conformal Metrics in f(R)-Gravity." International Journal of Analysis and Applications 23 (March 24, 2025): 76. https://doi.org/10.28924/2291-8639-23-2025-76.

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In this article, we explore certain almost conformal Ricci solitons in f(R)-gravity by assuming the potential vector field as a concircular vector field. We also study the almost conformal gradient-Ricci solitons and the almost conformal ω-Ricci solitons in f(R)-gravity. Furthermore, it is shown that an almost conformal ω-Ricci soliton and an almost conformal ω-Ricci-Yamabe soliton establish Poisson’s equation. At the last, some examples are constructed.

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37

Abolarinwa, Abimbola. "Gap theorems for compact almost Ricci-harmonic solitons." International Journal of Mathematics 30, no. 08 (2019): 1950040. http://dx.doi.org/10.1142/s0129167x1950040x.

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Almost Ricci-harmonic solitons are generalization of Ricci-harmonic solitons, almost Ricci solitons and harmonic-Einstein metrics. The main focus of this paper is to establish necessary and sufficient conditions for a gradient shrinking almost Ricci-harmonic soliton on a compact domain to be almost harmonic-Einstein.

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38

Mondal, Somnath, Santu Dey, Ali Alkhaldi, Ashis Sarkar та Arindam Bhattacharyya. "Geometry of almost *-η-Ricci-Yamabe soliton on Kenmotsu manifolds". Filomat 38, № 24 (2024): 8525–40. https://doi.org/10.2298/fil2424525m.

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The goal of the present object is to study almost *-?-Ricci-Yamabe soliton within the framework of Kenmotsu manifolds. It is shown that if a Kenmotsu manifold admits a *-?-Ricci-Yamabe soliton, then it is ?-Einstein. Next, we prove that if a (?,-2)?-nullity distribution, where ? <-1 acknowledges a *-?-Ricci-Yamabe soliton, then the manifold is Ricci flat. Later, if g represents a gradient almost *-?-Ricci-Yamabe soliton and ? leaves the scalar curvature r invariant on a Kenmotsu manifold, then the manifold is an ?-Einstein. Further, we have studied on a Kenmotsu manifold if g represents an

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Opferkuch, Toby, Pedro Schwaller, and Ben A. Stefanek. "Ricci reheating." Journal of Cosmology and Astroparticle Physics 2019, no. 07 (2019): 016. http://dx.doi.org/10.1088/1475-7516/2019/07/016.

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Alodan, Haila. "RICCI SOLITONS." JP Journal of Geometry and Topology 24, no. 1-2 (2020): 55–59. http://dx.doi.org/10.17654/gt024120055.

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VAGHEF, Mina, and Asadollah RAZAVI. "Stability of compact Ricci solitons under Ricci flow." TURKISH JOURNAL OF MATHEMATICS 39 (2015): 490–500. http://dx.doi.org/10.3906/mat-1406-4.

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Tabatabaeifar, Tayebeh, Behzad Najafi, and Akbar Tayebi. "Weighted projective Ricci curvature in Finsler geometry." Mathematica Slovaca 71, no. 1 (2021): 183–98. http://dx.doi.org/10.1515/ms-2017-0446.

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Abstract In this paper, we introduce the weighted projective Ricci curvature as an extension of projective Ricci curvature introduced by Z. Shen. We characterize the class of Randers metrics of weighted projective Ricci flat curvature. We find the necessary and sufficient condition under which a Kropina metric has weighted projective Ricci flat curvature. Finally, we show that every projectively flat metric with isotropic weighted projective Ricci and isotropic S-curvature is a Kropina metric or Randers metric.

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DIDA, Hamou Mohammed, and Fouzi HATHOUT. "Semi-symmetric types on hyperbolic Kenmotsu manifolds." General Letters in Mathematics 14, no. 3 (2024): 63–74. http://dx.doi.org/10.31559/glm2024.14.3.3.

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In this paper, we give some necessary conditions for an hyperbolic Kenmotsu manifolds M satisfying semi-symmetric, Ricci semi-symmetric, Weyl semi-symmetric and Einstein semi-symmetric. Next, we study the notion of n-Ricci soliton in context of hyperbolic Kenmotsu 3-manifolds M3 and we construct an example to illustrate the existence of n-Ricci soliton. Finally, we present some conditions to M admitting Codazzi type of Ricci tensor and cyclic n-recurrent Ricci tensor.

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Dey, S. "A study on conformal Ricci solitons and conformal Ricci almost solitons within the framework of almost contact geometry." Carpathian Mathematical Publications 15, no. 1 (2023): 31–42. http://dx.doi.org/10.15330/cmp.15.1.31-42.

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The goal of this paper is to find some important Einstein manifolds using conformal Ricci solitons and conformal Ricci almost solitons. We prove that a Kenmotsu metric as a conformal Ricci soliton is Einstein if it is an $\eta$-Einstein or the potential vector field $V$ is infinitesimal contact transformation or collinear with the Reeb vector field $\xi$. Next, we prove that a Kenmotsu metric as gradient conformal Ricci almost soliton is Einstein if the Reeb vector field leaves the scalar curvature invariant. Finally, we have embellished an example to illustrate the existence of conformal Ricc

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Honda, Shouhei. "On low-dimensional Ricci limit spaces." Nagoya Mathematical Journal 209 (March 2013): 1–22. http://dx.doi.org/10.1017/s0027763000010667.

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AbstractWe call a Gromov–Hausdorff limit of complete Riemannian manifolds with a lower bound of Ricci curvature a Ricci limit space. Furthermore, we prove that any Ricci limit space has integral Hausdorff dimension, provided that its Hausdorff dimension is not greater than 2. We also classify 1-dimensional Ricci limit spaces.

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Singh, Abhishek, та Shyam Kishor. "SOME TYPES OF η-RICCI SOLITONS ON LORENTZIAN PARA-SASAKIAN MANIFOLDS". Facta Universitatis, Series: Mathematics and Informatics 33, № 2 (2018): 217. http://dx.doi.org/10.22190/fumi1802217s.

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In this paper we study some types of η-Ricci solitons on Lorentzianpara-Sasakian manifolds and we give an example of η-Ricci solitons on 3-dimensional Lorentzian para-Sasakian manifold. We obtain the conditions of η-Ricci soliton on ϕ-conformally flat, ϕ-conharmonically flat and ϕ-projectivelyflat Lorentzian para-Sasakian manifolds, the existence of η-Ricci solitons implies that (M,g) is η-Einstein manifold. In these cases there is no Ricci solitonon M with the potential vector field

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Traore, Moctar, Hakan Mete Taştan та Sibel Gerdan Aydın. "On almost η-Ricci-Bourguignon solitons". Miskolc Mathematical Notes 25, № 1 (2024): 493. http://dx.doi.org/10.18514/mmn.2024.4378.

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We investigate a Riemannian manifold with almost η-Ricci-Bourguignon soliton structure. We use the Hodge-de Rham decomposition theorem to make a link with the associated vector field of an almost η-Ricci-Bourguignon soliton. Moreover, we show that a nontrivial, compact almost η-Ricci-Bourguignon soliton of constant scalar curvature is isometric to the Euclidean sphere. Using some results obtaining from almost η-Ricci Bourguignon soliton, we give the integral formulas for compact orientable almost η-Ricci-Bourguignon soliton.

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Sangeetha, M., та H. G. Nagaraja. "Geometry of Ricci and ( η , ω ) -Ricci solitons on the Sasaki–Kenmotsu manifold". Ukrains’kyi Matematychnyi Zhurnal 77, № 1 (2025): 77. https://doi.org/10.3842/umzh.v77i1.8084.

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UDC 514.7 We characterize the Sasaki–Kenmotsu manifold by using different kinds of solitons. Thus, we introduce a new type of solitons on the Sasaki–Kenmotsu manifold using a bicontact structure. First, we observe the properties of the Ricci soliton on ( η , ω ) -Sasaki–Kenmotsu manifold by using bicontact structure. Then we extended the η -Ricci soliton as an ( η , ω ) -Ricci soliton and a conformal η -Ricci soliton as a conformal ( η , ω ) -Ricci soliton by using the bicontact structure.

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KNOPF, DAN. "POSITIVITY OF RICCI CURVATURE UNDER THE KÄHLER–RICCI FLOW." Communications in Contemporary Mathematics 08, no. 01 (2006): 123–33. http://dx.doi.org/10.1142/s0219199706002052.

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In each complex dimension n ≥ 2, we construct complete Kähler manifolds of bounded curvature and non-negative Ricci curvature whose Kähler–Ricci evolutions immediately acquire Ricci curvature of mixed sign.

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Sardar, Arpan, Mohammad Nazrul Islam Khan та Uday Chand De. "η-∗-Ricci Solitons and Almost co-Kähler Manifolds". Mathematics 9, № 24 (2021): 3200. http://dx.doi.org/10.3390/math9243200.

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The subject of the present paper is the investigation of a new type of solitons, called η-∗-Ricci solitons in (k,μ)-almost co-Kähler manifold (briefly, ackm), which generalizes the notion of the η-Ricci soliton introduced by Cho and Kimura. First, the expression of the ∗-Ricci tensor on ackm is obtained. Additionally, we classify the η-∗-Ricci solitons in (k,μ)-ackms. Next, we investigate (k,μ)-ackms admitting gradient η-∗-Ricci solitons. Finally, we construct two examples to illustrate our results.

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