From the 2 of 8 linked papers with an AI index.
8 papers
Closed manifolds, model geometries, and volume related differentiable invariants
Santiago R. Simanca
The paper analyzes closed manifolds by studying their metrics via isometric embeddings, establishing criteria linking scalar curvature, Ricci curvature, and Kazdan‑Warner types, an…
Minimally embedded Riemann surfaces in $\mb{S}^3$ and the conformal deformation of their metrics
Santiago R. Simanca
The paper shows that any area‑preserving conformal deformation of a minimal isometric embedding of a surface into a sphere can be realized by a conformal diffeomorphism of the sphe…
Conformal properties of spheres
Santiago R. Simanca
We identify the smooth metrics $\mc{M}(M)$ on a manifold with the smooth isometric embeddings $f_g: (M,g) \rightarrow (\mb{S}^{\tn}, \tg)$ into a standard sphere of large dim…
Riemannian metric representatives of the Stiefel-Whitney classes
Santiago R Simanca
If is a closed manifold, and is a smooth triangulation of , Whitney proved that all of the Stiefel-Whitney classes are specified as cochains on the dual cell complex $(K…
The sigma invariant of the torus, the K3 surface, and Euclidean and elliptic 3d manifolds
Santiago R. Simanca
On the space of isometric embeddings of metrics on a manifold into the standard $(\mb{S}^{\tn=\tn(n)},\tg)$, we consider the total exterior scalar curvature$Θ_{f_g}…
Vector field cycles in the tangent bundle
Santiago R. Simanca
Given a closed Riemannian manifold and a vector field on , we form the Sasaki metric on , and restrict it to the image of the cross section map of in…