Space of Nonnegatively Curved Metrics and Pseudoisotopies
نویسنده
چکیده
Let V be an open manifold with complete nonnegatively curved metric such that the normal sphere bundle to a soul has no section. We prove that the souls of nearby nonnegatively curved metrics on V are smoothly close. Combining this result with some topological properties of pseudoisotopies we show that for many V the space of complete nonnegatively curved metrics has infinite higher homotopy groups.
منابع مشابه
Techniques for Classifying Nonnegatively Curved Left-invariant Metrics on Compact Lie Groups
We provide techniques for studying the nonnegatively curved leftinvariant metrics on a compact Lie group. For “straight” paths of left-invariant metrics starting at bi-invariant metrics and ending at nonnegatively curved metrics, we deduce a nonnegativity property of the initial derivative of curvature. We apply this result to obtain a partial classification of the nonnegatively curved left-inv...
متن کاملVector Bundles with Infinitely Many Souls
We construct the first examples of manifolds, the simplest one being S3×S4×R5, which admit infinitely many complete nonnegatively curved metrics with pairwise nonhomeomorphic souls. According to the soul theorem of J. Cheeger and D. Gromoll [CG72], a complete open manifold of nonnegative sectional curvature is diffeomorphic to the total space of the normal bundle of a compact totally geodesic s...
متن کاملm at h . D G ] 2 3 Ju n 20 08 HOMOGENEOUS METRICS WITH NONNEGATIVE CURVATURE
Given compact Lie groups H ⊂ G, we study the space of G-invariant metrics on G/H with nonnegative sectional curvature. For an intermediate subgroup K between H and G, we derive conditions under which enlarging the Lie algebra of K maintains nonnegative curvature on G/H . Such an enlarging is possible if (K, H) is a symmetric pair, which yields many new examples of nonnegatively curved homogeneo...
متن کاملRigidity for Nonnegatively Curved Metrics
We address the question: how large is the family of complete metrics with nonnegative sectional curvature on S × R? We classify the connection metrics, and give several examples of non-connection metrics. We provide evidence that the family is small by proving some rigidity results for metrics more general than connection metrics.
متن کاملRigidity for Nonnegatively Curved Metrics on S × R
We address the question: how large is the family of complete metrics with nonnegative sectional curvature on S2 × R3? We classify the connection metrics, and give several examples of non-connection metrics. We provide evidence that the family is small by proving some rigidity results for metrics more general than connection metrics.
متن کامل