Results 21 to 30 of about 2,635 (149)
Isometry theorem of gradient Shrinking Ricci solitons [PDF]
Journal of Geometry and Physics, 2021 In this paper, we have proved that if a complete conformally flat gradient shrinking Ricci soliton has linear volume growth or the scalar curvature is finitely integrable and also the reciprocal of the potential function is subharmonic, then the manifold is isometric to the Euclidean sphere.
Shaikh, Absos Ali, Mondal, Chandan Kumar
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TURKISH JOURNAL OF MATHEMATICS, 2020 The classical notion of gradient Ricci soliton is extended here to the gradient Weyl-Ricci soliton. A Weyl structureofthebasemanifold M is lifted to its tangent bundle TM, by using the Sasaki metric. We give some necessary and sufficient conditions such that the Weyl structure on TM to be a gradient Weyl-Ricci soliton.
Cornelia-Livia BEJAN +2 more
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The curvature of gradient Ricci solitons [PDF]
Mathematical Research Letters, 2011 We study integral and pointwise bounds on the curvature of gradient shrinking Ricci solitons. As applications we discuss gap and compactness results for gradient shrinkers.
Munteanu, Ovidiu, Wang, Mu-Tao
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On Bach-flat gradient shrinking Ricci solitons [PDF]
, 2012 In this paper, we classify n-dimensional (n>3) complete Bach-flat gradient shrinking Ricci solitons. More precisely, we prove that any 4-dimensional Bach-flat gradient shrinking Ricci soliton is either Einstein, or locally conformally flat hence a finite
Cao, Huai-Dong, Chen, Qiang
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Journal of Geometric Analysis, 2011 to appear in J.
Munteanu, Ovidiu, Sesum, Natasa
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INEQUALITIES FOR GRADIENT EINSTEIN AND RICCI SOLITONS [PDF]
Facta Universitatis, Series: Mathematics and Informatics, 2020 This short note concerns with two inequalities in the geo\-me\-try of gradient Einstein solitons $(g, f, \lambda )$ on a smooth manifold $M$. These inequalities provide some relationships between the curvature of the Riemannian metric $g$ and the behavior of the scalar field $f$ through two quadratic equations satisfied by the scalar $\lambda $.
Blaga, Adara-Monica, Crasmareanu, Mircea
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On gradient Ricci solitons with symmetry [PDF]
Proceedings of the American Mathematical Society, 2009 We study gradient Ricci solitons with maximal symmetry. First we show that there are no nontrivial homogeneous gradient Ricci solitons. Thus, the most symmetry one can expect is an isometric cohomogeneity one group action. Many examples of cohomogeneity one gradient solitons have been constructed.
Petersen, Peter, Wylie, William
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Geometric classifications of k-almost Ricci solitons admitting paracontact metrices
Open Mathematics, 2023 The prime objective of the approach is to give geometric classifications of kk-almost Ricci solitons associated with paracontact manifolds. Let M2n+1(φ,ξ,η,g){M}^{2n+1}\left(\varphi ,\xi ,\eta ,g) be a paracontact metric manifold, and if a KK-paracontact
Li Yanlin +4 more
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Locally conformally flat ancient Ricci flows [PDF]
, 2015 We show that any locally conformally flat ancient solution to the Ricci flow must be rotationally symmetric. As a by-product, we prove that any locally conformally flat Ricci soliton is a gradient soliton in the shrinking and steady cases as well as in ...
Catino, Giovanni +2 more
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Rigidity of Complete Gradient Shrinkers with Pointwise Pinching Riemannian Curvature
Advances in Mathematical Physics, 2021 Let Mn,g,f be a complete gradient shrinking Ricci soliton of dimension n≥3. In this paper, we study the rigidity of Mn,g,f with pointwise pinching curvature and obtain some rigidity results.
Yawei Chu, Dehe Li, Jundong Zhou
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