Results 21 to 30 of about 148 (141)
Two-Dimensional Gradient Ricci Solitons Revisited [PDF]
International Mathematics Research Notices, 2013 In this note, we complete the classification of the geometry of non-compact two-dimensional gradient Ricci solitons. As a consequence, we obtain two corollaries: First, a complete two-dimensional gradient Ricci soliton has bounded curvature. Second, we give examples of complete two-dimensional expanding Ricci solitons with negative curvature that are ...
Bernstein, Jacob, Mettler, Thomas
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Stability of gradient Kähler-Ricci solitons [PDF]
Communications in Analysis and Geometry, 2005 We study stability of non-compact gradient Kaehler-Ricci flow solitons with positive holomorphic bisectional curvature. Our main result is that any compactly supported perturbation and appropriately decaying perturbations of the Kaehler potential of the soliton will converge to the original soliton under Kaehler-Ricci flow as time tends to infinity. To
Chau, Albert, Schnuerer, Oliver C.
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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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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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Gradient Kähler–Ricci solitons and periodic orbits [PDF]
Communications in Analysis and Geometry, 2000 We study Hamiltonian dynamics of gradient Kaehler-Ricci solitons that arise as limits of dilations of singularities of the Ricci flow on compact Kaehler manifolds. Our main result is that the underlying spaces of such gradient solitons must be Stein manifolds.
Cao, Huai-Dong, Hamilton, Richard S.
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Volume Growth Estimates of Gradient Ricci Solitons
The Journal of Geometric Analysis, 2022 AbstractIn this paper, we survey the volume growth estimates for shrinking, steady, and expanding gradient Ricci solitons. Together with the known results, we also prove some new volume growth estimates for expanding gradient Ricci solitons.
Pak-Yeung Chan, Zilu Ma, Yongjia Zhang
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