An orbit space of a nonlinear involution of $S^2\times S^2$ with nonnegative sectional curvature

Rafael Torres

An orbit space of a nonlinear involution of $S^2\times S^2$ with nonnegative sectional curvature

Differential Geometry 2018-12-14 v3

Authors: Rafael Torres

Abstract

We describe a construction of Riemannian metrics of nonnegative sectional curvature on a closed smooth nonorientable 4-manifold with fundamental group of order two that realizes a homotopy class that was not previously known to contain nonnegatively curved manifolds. The procedure yields new metrics of nonnegative sectional curvature on any 2-sphere bundle with base space the 2-sphere or the real projective plane.

Keywords

orbit space nonlinear involution nonnegative sectional curvature Riemannian metrics nonorientable 4-manifold 2-sphere bundle homotopy class

Cite

@article{arxiv.1506.01578,
  title  = {An orbit space of a nonlinear involution of $S^2\times S^2$ with nonnegative sectional curvature},
  author = {Rafael Torres},
  journal= {arXiv preprint arXiv:1506.01578},
  year   = {2018}
}

Comments

v3: Renato Bettiol kindly pointed out to us a mistake in v2: the gluing diffeomorphism was NOT an isometry of the chosen metrics on the disk bundles. This version corrects the mistake. New title reflects that the paper has been completely rewritten having only the four-dimensional scenario as a case study

An orbit space of a nonlinear involution of $S^2\times S^2$ with nonnegative sectional curvature

Abstract

Keywords

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