Almost Nonnegative Curvature on Some Fake $RP^{6}s$ and $RP^{14}s$

TL;DR

This paper demonstrates the construction of metrics with almost nonnegative curvature on certain fake real projective spaces, extending the understanding of curvature properties in differential geometry.

Contribution

It applies a lifting theorem to establish almost nonnegative curvature metrics on specific fake real projective spaces, advancing geometric analysis techniques.

Findings

Metrics of almost nonnegative curvature constructed on fake RP^6 and RP^14

Extension of curvature results to new classes of fake projective spaces

Utilization of the lifting theorem in geometric metric construction

Abstract

We apply the lifting theorem of Searle and the second author to put metrics of almost nonnegative curvature on the fake RP^{6}s of Hirsch and Milnor and on the analogous fake RP^{14}s.