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A note on static manifolds and almost Ricci solitons
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In this short paper, we investigate the existence of non-trivial almost Ricci solitones on static manifolds. As a result we show any compact nontrivial static manifold is isometric to a Euclidean sphere.
Abstract
In this short paper, we investigate the existence of non-trivial almost Ricci solitones on static manifolds. As a result we show any compact nontrivial static manifold is isometric to a Euclidean sphere.
참고문헌 (6)
- A. Barros, "Compact almost Ricci solitons with constant scalar curvature are gradient", Monatshefte für Mathematik, 174(1), pp.29~39 (2013), Springer Science and Business Media LLC[DOI]
- Justin Corvino, "Scalar Curvature Deformation and a Gluing Construction for the Einstein Constraint Equations", Communications in Mathematical Physics, 214(1), pp.137~189 (2000), Springer Science and Business Media LLC[DOI]
- Junfang Li, "An Integral Formula for Affine Connections", The Journal of Geometric Analysis, 27(3), pp.2539~2556 (2017), Springer Science and Business Media LLC[DOI]
- S. Pigola, "Ricci almost solitons", Ann. Sc. Norm. Super. Pisa Cl. Sci, 10(4), pp.757~799 (2011)
- Jie Qing, "On scalar curvature rigidity of vacuum static spaces", Mathematische Annalen, 365(3-4), pp.1257~1277 (2015), Springer Science and Business Media LLC[DOI]
- Xiaodong Wang, "Brendle’s Inequality on Static Manifolds", The Journal of Geometric Analysis, 28(1), pp.152~169 (2017), Springer Science and Business Media LLC[DOI]
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