On manifolds with nonnegative curvature on totally isotropic 2-planes
نویسندگان
چکیده
منابع مشابه
Manifolds with Nonnegative Isotropic Curvature
We prove that if (M, g) is a compact locally irreducible Riemannian manifold with nonnegative isotropic curvature, then one of the following possibilities hold: (i) M admits a metric with positive isotropic curvature (ii) (M, g) is isometric to a locally symmetric space (iii) (M, g) is Kähler and biholomorphic to CP n. This is implied by the following two results: (i) Let (M, g) be a compact, l...
متن کاملOn the Smooth Rigidity of Almost-einstein Manifolds with Nonnegative Isotropic Curvature
Let (Mn, g), n ≥ 4, be a compact simply-connected Riemannian manifold with nonnegative isotropic curvature. Given 0 < l ≤ L, we prove that there exists ε = ε(l, L, n) satisfying the following: If the scalar curvature s of g satisfies l ≤ s ≤ L and the Einstein tensor satisfies |Ric − s n g| ≤ ε then M is diffeomorphic to a symmetric space of compact type. This is a smooth analogue of the result...
متن کاملOn the Complex Structure of Kähler Manifolds with Nonnegative Curvature
We study the asymptotic behavior of the Kähler-Ricci flow on Kähler manifolds of nonnegative holomorphic bisectional curvature. Using these results we prove that a complete noncompact Kähler manifold with nonnegative bounded holomorphic bisectional curvature and maximal volume growth is biholomorphic to complex Euclidean space C . We also show that the volume growth condition can be removed if ...
متن کاملBoundary Convexity on Manifolds with Nonnegative Ricci Curvature
We introduce a new geometric invariant Λ to measure the convexity of the boundary of a riemannian manifold with nonnegative Ricci curvature in the interior. Based on a theorem of Perelman, we are able to show that this new invariant has topological implications. More specifically, we show that if Λ is close to 1 and the sectional curvature is positive on the boundary, then the manifold is contr...
متن کاملOn the Metric Structure of Open Manifolds with Nonnegative Curvature
An open manifold M with nonnegative sectional curvature contains a compact totally geodesic submanifold S called the soul. In his solution of the Cheeger-Gromoll conjecture, G. Perelman showed that the metric projection π : M → S was a C Riemannian submersion which coincided with a map previously constructed by V. Sharafutdinov. In this paper we improve Perelman’s result to show that π is in fa...
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: Transactions of the American Mathematical Society
سال: 1993
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-1993-1123458-2