106 citations · 125 across the 21 of their papers we have counts for
23 papers
Closed manifolds, model geometries, and volume related differentiable invariants
Santiago R. Simanca
We view metrics through their isometric embeddigns $f_g:(M^n,g)\rightarrow (\mb{S}^{\tn},\tg)$ and their deformations. If carries a metric of constant scalar curvature $s_g…
Minimally embedded Riemann surfaces in $\mb{S}^3$ and the conformal deformation of their metrics
Santiago R. Simanca
We prove that if $f_g: (Σ,g) \rightarrow (\mb{S}^{2+p},\tg)$ is a smooth minimal isometric embedding of a Riemannian surface , and is a path of…
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…
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…
On some manifolds with positive sigma invariants and their realizing conformal classes
Santiago R. Simanca
We prove that the metric of the Riemannian product $(\mb{S}^k(r_1)\times \mb{S}^{n-k}(r_2), g^n_k)$, , is a Yamabe metric in its conformal class if, and only if, eit…