Einstein manifolds with zero Ricci curvature
نویسندگان
چکیده
منابع مشابه
Ricci Curvature Bounds and Einstein Metrics on Compact Manifolds
dL(Mo,M1) = inf[llogdil/l + Ilogdil/-II], f where I: Mo -+ MI is a homeomorphism and dil I is the dilatation of I given by dill = SUPXt#2 dist(f(x l ), l(x2))/ dist(x1 ,x2). If Mo and MI are not homeomorphic, define dL(Mo,M1) = +00. Gromov [20] proves the remarkable result that the space of compact Riemannian manifolds L(A,t5 ,D) of sectional curvature IKI :::; A, injectivity radius i M 2: t5 >...
متن کاملHighly connected manifolds with positive Ricci curvature
We prove the existence of Sasakian metrics with positive Ricci curvature on certain highly connected odd dimensional manifolds. In particular, we show that manifolds homeomorphic to the 2k-fold connected sum of S × S admit Sasakian metrics with positive Ricci curvature for all k. Furthermore, a formula for computing the diffeomorphism types is given and tables are presented for dimensions 7 and...
متن کاملRicci flow and manifolds with positive curvature
This is an expository article based on the author’s lecture delivered at the conference Lie Theory and Its Applications in March 2011, UCSD. We discuss various notions of positivity and their relations with the study of the Ricci flow, including a proof of the assertion, due to Wolfson and the author, that the Ricci flow preserves the positivity of the complex sectional curvature. We discuss th...
متن کاملConformally Flat Manifolds with Nonnegative Ricci Curvature
We show that complete conformally flat manifolds of dimension n > 3 with nonnegative Ricci curvature enjoy nice rigidity properties: they are either flat, or locally isometric to a product of a sphere and a line, or are globally conformally equivalent to R n or a spherical spaceform Sn/Γ. This extends previous results due to Q.-M. Cheng and B.-L. Chen and X.-P. Zhu. In this note, we study compl...
متن کاملHomogeneous symplectic manifolds with Ricci - type curvature
We consider invariant symplectic connections ∇ on homogeneous symplectic manifolds (M, ω) with curvature of Ricci type. Such connections are solutions of a variational problem studied by Bourgeois and Cahen, and provide an integrable almost complex structure on the bundle of almost complex structures compatible with the symplectic structure. If M is compact with finite fundamental group then (M...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Surveys in Differential Geometry
سال: 2001
ISSN: 1052-9233,2164-4713
DOI: 10.4310/sdg.2001.v6.n1.a1