Zobrazeno 1 - 10
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pro vyhledávání: '"Simanca, Santiago R."'
Autor:
Simanca, Santiago R.
We identify the cone of smooth metrics $\mc{M}(M)$ on a manifold $M^n$ with the space of smooth isometric embeddings $f_g: (M,g) \rightarrow (\mb{S}^{\tn},\tg)$ into a standard sphere of large dimension $\tn=\tn(n)$, and their isotopic deformations,
Externí odkaz:
http://arxiv.org/abs/2405.16014
Autor:
Simanca, Santiago R.
We prove that the metric of the Riemannian product $(\mb{S}^k(r_1)\times \mb{S}^{n-k}(r_2), g^n_k)$, $r_1^2+r_2^2=1$, is a Yamabe metric in its conformal class if, and only if, either $g^n_k$ is Einstein, or the linear isometric embedding of this man
Externí odkaz:
http://arxiv.org/abs/2311.05123
Autor:
Simanca, Santiago R.
We view all smooth metrics $g$ on a closed surface $\Sigma$ through their Nash isometric embeddings $f_g: (\Sigma,g) \rightarrow (\mathbb{S}^{\tilde{n}}, \tilde{g})$ into a standard sphere of large, but fixed, dimension $\tilde{n}$. We define the Wil
Externí odkaz:
http://arxiv.org/abs/2303.17793
Autor:
Simanca, Santiago R
We identify all metrics on a closed $n$-manifold with their Nash isometric embeddings into a standard sphere of large, but fixed dimension, and use the Palais' isotopic extension theorem to identify their deformations with the isotopic deformations o
Externí odkaz:
http://arxiv.org/abs/2204.12628
Autor:
Simanca, Santiago R
We describe the equations of motion of an incompressible elastic body $\Omega$ in 3-space acted on by an external pressure force, and the Newton iteration scheme that proves the well-posedness of the resulting initial value problem for its equations
Externí odkaz:
http://arxiv.org/abs/2007.03457
Autor:
Simanca, Santiago R
If $M$ is a closed manifold, and $K$ is a smooth triangulation of $M$, Whitney proved that all of the Stiefel-Whitney classes are specified as cochains on the dual cell complex $(K')^*$ assigning the value $1$ mod $2$ to each dual cell. We provide th
Externí odkaz:
http://arxiv.org/abs/2004.05719
Autor:
Simanca, Santiago R
On a given closed connected manifold of dimension two, or greater, we consider the squared $L^2$-norm of the scalar curvature functional over the space of constant volume Riemannian metrics. We prove that its critical points have constant scalar curv
Externí odkaz:
http://arxiv.org/abs/1911.02706
Autor:
Simanca, Santiago R
We define inductively isometric embeddings of $\mb{P}^n(\mb{R})$ and $\mb{P}^n(\mb{C})$ (with their canonical metrics conveniently scaled) into the standard unit sphere, which present the former as the restriction of the latter to the set of real poi
Externí odkaz:
http://arxiv.org/abs/1812.10173
Autor:
Simanca, Santiago R.
We describe the equations of motion of elastodynamic bounded bodies in 3-space, and their linearizations at a stationary point. Using the latter as an approximation to model small motions, we develop a scheme to find numerical solutions of these equa
Externí odkaz:
http://arxiv.org/abs/1805.05460
Autor:
Simanca, Santiago R.
We consider critical points of the global squared $L^2$-norms of the second fundamental form and the mean curvature vector of isometric immersions into a fixed background Riemannian manifold under deformations of the immersion. We use the critical po
Externí odkaz:
http://arxiv.org/abs/1501.00164