nLab p-curvature

Idea

In Riemannian geometry the term $p$-curvature (Labbi 97) refers to a generalization of the scalar curvature.

Related entries

curvature in Riemannian geometry
Riemann curvature
Ricci curvature
scalar curvature
sectional curvature
p-curvature

• Stolz conjecture

References

In Riemannian geometry

The concept was introduced in

• Mohammed Labbi, Stability under surgeries of the $p$-curvature positivity and manifolds with positive Einstein tensor, Annals of Global Analysis and Geometry, 15 no 4, 299-312 (1997). (pdf)

Further discussion includes

• Mohammed Labbi, Manifolds with positive second Gauss-Bonnet curvature, Pacific Journal of Math. Vol. 227, No. 2, 295-310, (2006) (pdf)

• Boris Botvinnik, Mohammed Labbi, Highly connected manifolds of positive $p$-curvature, Transactions of the AMS, Trans. Amer. Math. Soc. 366 (2014), 3405-3424 (arXiv:1201.1849, doi:10.1090/S0002-9947-2014-05939-4)

(see also at fivebrane structure).

In algebraic geometry

• Brian Osserman, Connections, curvature and $p$-curvature (pdf)