Extension of Symmetries on Einstein Manifolds with Boundary
نویسنده
چکیده
We investigate the isometry extension property for Einstein metrics on manifolds with boundary; namely when Killing fields of the boundary metric extend to Killing fields of any filling Einstein metric. Applications to Bartnik’s static extension conjecture are also discussed.
منابع مشابه
Conformal mappings preserving the Einstein tensor of Weyl manifolds
In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...
متن کاملErratum To: Extension of Symmetries on Einstein Manifolds with Boundary
In this note, we point out and correct an error in the proof of Theorem 1.1 in [1]. All of the main results of [1] are correct as stated but the proofs require modification. We use below the same notation as in [1]. ∂M (δ * Y)(N, X) = 0, cannot always be simultaneously enforced with the slice property [1, (5.7)], i.e.
متن کاملWarped product and quasi-Einstein metrics
Warped products provide a rich class of physically significant geometric objects. Warped product construction is an important method to produce a new metric with a base manifold and a fibre. We construct compact base manifolds with a positive scalar curvature which do not admit any non-trivial quasi-Einstein warped product, and non compact complete base manifolds which do not admit any non-triv...
متن کاملOn Lorentzian two-Symmetric Manifolds of Dimension-four
‎We study curvature properties of four-dimensional Lorentzian manifolds with two-symmetry property‎. ‎We then consider Einstein-like metrics‎, ‎Ricci solitons and homogeneity over these spaces‎‎.
متن کاملHidden Symmetries of Euclideanised Kerr-NUT-(A)dS Metrics in Certain Scaling Limits
The hidden symmetries of higher dimensional Kerr-NUT-(A)dS metrics are investigated. In certain scaling limits these metrics are related to the Einstein–Sasaki ones. The complete set of Killing–Yano tensors of the Einstein–Sasaki spaces are presented. For this purpose the Killing forms of the Calabi–Yau cone over the Einstein–Sasaki manifold are constructed. Two new Killing forms on Einstein–Sa...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008