English

Gluing Riemannian manifolds with curvature operators at least k

Differential Geometry 2012-10-11 v1

Abstract

We glue two manifolds which have curvature operators at least k (in the sense of eigenvalues) along their common boundary. We show that if the sum of the second fundamental forms of the boundary is positive semidefinite, then the curvature operator of the resulting manifold is at least k up to an arbitrarily small error term. Similar results hold for Ricci, scalar, bi, isotropic and flag curvature, respectively.

Keywords

Cite

@article{arxiv.1210.2957,
  title  = {Gluing Riemannian manifolds with curvature operators at least k},
  author = {Arthur Schlichting},
  journal= {arXiv preprint arXiv:1210.2957},
  year   = {2012}
}