Robert L. Bryant

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math.DG2024

Hessianizability of surface metrics

Robert L. Bryant

A symmetric quadratic form $g$ on a surface~ $M$ is said to be locally Hessianizable if each $p \in M$ has an open neighborhood~ $U$ on which there exists a local coordinate chart $(x…

math.DG2024

Curvature homogeneous hypersurfaces in space forms

Robert Bryant, Luis Florit, Wolfgang Ziller

We classify curvature homogeneous hypersurfaces in S^4 and H^4. In higher dimesnsion one only has the FKM examples and an isolate one by Tsukada of a hypersurface in H^5. Besides s…

math.DG2023

The generality of closed $G_{2}$ solitons

Robert L. Bryant

The local generality of the space of solitons for the Laplacian flow of closed $G_{2}$ -structures is analyzed, and it is shown that the germs of such structures depend, up to diffeom…

Hessianizability of surface metrics

Curvature homogeneous hypersurfaces in space forms

The generality of closed G2​ solitons

The generality of closed $G_{2}$ solitons