A variational approach for compact homogeneous Einstein manifolds

By Christoph Böhm, Mckenzie Y. Wang, W. Ziller. 2004

168 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2e917ae4a592bfc83d636a11d2a4d7a090cb98ee

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In Applied Mathematics

In Astronomy and Astrophysics

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Citations in the corpus

Classification of generalized Wallach spaces (2014, background): “More detailed information on invariant Einstein metric on general homogeneous spaces could be found in [4–6,23,24].”
Linear stability of Perelman's $ν$-entropy on symmetric spaces of compact type (2013, methodology): “ely the negative of the traceless Ricci tensor. This variational approach of ﬁnding Einstein metrics, for example on compact homogeneous spaces, has been studied by C. B¨ohm, M. Wang and W. Ziller in [BWZ]. It is well-known that the second variation of the Hilbert action on the standard spheres vani”
Ricci flow of homogeneous manifolds (2011, background): “e is just a system of n(n+1) 2 algebraic equations, but unfortunately, quite an involved one, and it is still open the question of which homogeneous spaces G=Kadmit a G-invariant Einstein metric (see [BWZ04, L09] and the references therein). In the noncompact homogeneous case, the only known nonat e”
The geometry of compact homogeneous spaces with two isotropy summands (2008, background): “For these spaces, the associated graph and complex of [3 ]a nd [ 5 ] is trivial.”
Bifurcation and local rigidity of homogeneous solutions to the Yamabe problem on spheres (2011, methodology): “ites from global analysis, the variational approach to the Yamabe problem and elementary properties of the Hilbert-Einstein functional. Most results discussed in this section are well-known, see e.g. [9,20,24,37]. Henceforth, Mdenotes a smooth closed (i.e., compact and without boundary) manifold of ”
Ricci soliton solvmanifolds (2010, background): “question: Which homogeneous manifolds G/K admit a G-invariant Ricci soliton metric? RICCI SOLITON SOLVMANIFOLDS 3 Unfortunately, even Einstein homogeneous manifolds are still not well understood (see [BWZ] and [L4] for the compact and noncompact cases, respectively). But let us ﬁrst review to what e”