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We study rigidity results for the Einstein metrics as the critical points of a family of known quadratic curvature functionals involving the scalar curvature, the Ricci curvature and the Riemannian curvature tensor, characterized by some pointwise inequalities involving the Weyl curvature and the traceless Ricci curvature. Moreover, we also provide a few rigidity results for locally conformally flat critical metrics.
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참고문헌 (22)
참고문헌 신청
Michael T. Anderson / 1997 / Extrema of curvature functionals on the space of metrics on 3-manifolds / Calculus of Variations and Partial Differential Equations 5(3):199~269
A. Barros / 2017 / On locally conformally flat critical metrics for quadratic functionals / Annals of Global Analysis and Geometry 52(1):1~9
A. L. Besse / 1987 / Einstein Manifolds, Classics in Mathematics / Springer-Verlag
Huai-Dong Cao / 2013 / On Bach-flat gradient shrinking Ricci solitons / Duke Mathematical Journal 162(6):1149~1169
G. Catino / 2016 / On conformally at manifolds with constant positive scalar curvature / Proc. Amer. Math. Soc 144(6):2627~2634
A. Barros / 2017 / On locally conformally flat critical metrics for quadratic functionals / Annals of Global Analysis and Geometry 52(1):1~9
A. L. Besse / 1987 / Einstein Manifolds, Classics in Mathematics / Springer-Verlag
Huai-Dong Cao / 2013 / On Bach-flat gradient shrinking Ricci solitons / Duke Mathematical Journal 162(6):1149~1169
G. Catino / 2016 / On conformally at manifolds with constant positive scalar curvature / Proc. Amer. Math. Soc 144(6):2627~2634
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