On the classification of three-dimensional compact Kaehler manifolds of nonnegative bisectional curvature
نویسندگان
چکیده
منابع مشابه
Compact Kähler Manifolds with Nonpositive Bisectional Curvature
Let (Mn, g) be a compact Kähler manifold with nonpositive bisectional curvature. We show that a finite cover is biholomorphic and isometric to a flat torus bundle over a compact Kähler manifold Nk with c1 < 0. This confirms a conjecture of Yau. As a corollary, for any compact Kähler manifold with nonpositive bisectional curvature, the Kodaira dimension is equal to the maximal rank of the Ricci ...
متن کاملRigidity of Compact Manifolds with Boundary and Nonnegative Ricci Curvature
Let Ω be an (n + 1)-dimensional compact Riemannian manifold with nonnegative Ricci curvature and nonempty boundary M = ∂Ω. Assume that the principal curvatures of M are bounded from below by a positive constant c. In this paper, we prove that the first nonzero eigenvalue λ1 of the Laplacian of M acting on functions on M satisfies λ1 ≥ nc2 with equality holding if and only if Ω is isometric to a...
متن کاملA Monotonicity Formula on Complete Kähler Manifolds with Nonnegative Bisectional Curvature
In [Y], Yau proposed to study the uniformization of complete Kähler manifolds with nonnegative curvature. In particular, one wishes to determine whether or not a complete Kähler manifold M with positive bisectional curvature is biholomorphic to C. See also [GW], [Si]. For this sake, it was further asked in [Y] whether or not the ring of the holomorphic functions with polynomial growth, which we...
متن کاملRicci flow on compact Kähler manifolds of positive bisectional
where ω̃ = ( √ −1/2)g̃ij̄dz ∧ dz and Σ̃ = ( √ −1/2)R̃ij̄dz ∧ dz are the Kähler form, the Ricci form of the metric g̃ respectively, while c1(M) denotes the first Chern class. Under the normalized initial condition (2), the first author [3] (see also Proposition 1.1 in [4]) showed that the solution g(x, t) = ∑ gij̄(x, t)dz dz to the normalized flow (1) exists for all time. Furthermore by the work of Mok ...
متن کاملThe Sasaki-ricci Flow and Compact Sasaki Manifolds of Positive Transverse Holomorphic Bisectional Curvature
We show that Perelman’s W functional on Kahler manifolds has a natural counterpart on Sasaki manifolds. We prove, using this functional, that Perelman’s results on Kahler-Ricci flow (the first Chern class is positive) can be generalized to Sasaki-Ricci flow, including the uniform bound on the diameter and the scalar curvature along the flow. We also show that positivity of transverse bisectiona...
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: Journal of Differential Geometry
سال: 1984
ISSN: 0022-040X
DOI: 10.4310/jdg/1214438680