Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 20 (2024), 038, 25 pages      arXiv:2306.02932
Contribution to the Special Issue on Differential Geometry Inspired by Mathematical Physics in honor of Jean-Pierre Bourguignon for his 75th birthday

Product Inequalities for $\mathbb T^\rtimes$-Stabilized Scalar Curvature

Misha Gromov ab
a) Courant Institute of Mathematical Sciences, New York University, New York, NY 10012-1185, USA
b) Institut des Hautes Études Scientifiques, 91893 Bures-sur-Yvette, France

Received June 26, 2023, in final form April 26, 2024; Published online May 08, 2024

We study metric invariants of Riemannian manifolds $X$ defined via the $\mathbb T^\rtimes$-stabilized scalar curvatures of manifolds $Y$ mapped to $X$ and prove in some cases additivity of these invariants under Riemannian products $X_1\times X_2$.

Key words: scalar curvature; Riemannian manifold.

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