I am currently studying the techniques related to geometry of positive and non-negative sectional curvature of Riemannian metrics. In particular, I have done some work with Cheeger deformations. I started to wonder:

On the context of semi-Riemannian metrics, is there restrictive conditions for positive and non-negative sectional curvature? (I know that there are restrictions on defining sectional curvature on this context, since there are degenerated planes, I am wondering about sectional curvature where it is well defined).

It seems to me that is rather delicate how to work with isometries groups of semi-Riemannian metrics and their actions. Is there any hope that the standard techniques of Cheeger deformations apply with small modifications on this context, considering the validity of the first question?

Thanks in advance

  • 1
    $\begingroup$ On how to define sectional curvature bounds (and their characterization via triangle comparison) I can recommend: S. Alexander, R.L. Bishop: Lorentz and semi-Riemannian spaces with Alexandrov curvature bounds, Comm. Anal. Geom. 16 (2008), 251-282 (faculty.math.illinois.edu/~sba/lor.pdf). I do not know about Cheeger deformations tough. $\endgroup$ – Clemens Sämann Aug 18 '18 at 5:58

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