Robert Bryant

Preprint · May 11, 2024 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 $(x^1,x^2):U\to\mathbb{R}^2$ and a function $f:U\to\mathbb{R}$ such that, on $U ... Link to item Cite

Curvature homogeneous hypersurfaces in space forms

Preprint · April 2, 2024 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 some simple examples, we show that there exists an isolated hypersurface wi ... Open Access Link to item Cite