106 citations · 125 across the 21 of their papers we have counts for
17 papers · 1 filter
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…