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R-critical Weyl structures
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Abstract
Weyl structures can be viewed as generalizations of Riemannian metrics. We study Weyl structures which are critical points of the squared $L^2$ norm functional of the full curvature tensor, defined on the space of Weyl structures on a compact 4-manifold. We find some relationship between these critical Weyl structures and the critical Riemannian metrics. Then in a search for homogeneous critical structures we study left-invariant metrics on some solv-manifolds and prove that they are not critical.
관련 논문AI추천
Conformal Transformations of a Weyl ManifoldFumio Narita, Takafumi Satou경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2004 · 제44권 제1호Critical points and warped product metrics장정욱, 황승수대한수학회 · 대한수학회보2004 · 제41권 제1호The critical point equation on a four dimensional warped product manifold장정욱, 황승수대한수학회 · 대한수학회보2006 · 제43권 제4호Locally homogeneous critical metrics on four-dimensional manifolds강유태대한수학회 · 대한수학회지2007 · 제44권 제1호Conformally Flat Quasi-Einstein SpacesDiptiman Saha, Joydeep Sengupta, Uday Chand De경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2006 · 제46권 제3호Some rigidity characterizations of Einstein metrics as critical points for quadratic curvature functionalsBingqing Ma, Guangyue Huang, Jie Yang대한수학회 · 대한수학회보2020 · 제57권 제6호
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