Zobrazeno 1 - 10
of 35
pro vyhledávání: '"Sinha, Raúl Oset"'
Autor:
Ribes, Ignacio Breva, Sinha, Raúl Oset
We give two characterisations of when a map-germ admits a 1-parameter stable unfolding, one related to the $\mathscr K_e$-codimension and another related to the normal form of a versal unfolding. We then prove that there are infinitely many finitely
Externí odkaz:
http://arxiv.org/abs/2410.10321
Autor:
Ribes, Ignacio Breva, Sinha, Raúl Oset
For function germs $g:(\mathbb C^n,0)\to (\mathbb C,0)$ it is well known that $1\leq\frac{\mu(g)}{\tau(g)}$ and it has recently been proved by Liu that $\frac{\mu(g)}{\tau(g)}\leq n$. We give an upper bound for the codimension of map-germs $f:(\mathb
Externí odkaz:
http://arxiv.org/abs/2305.13811
We refine the affine classification of real nets of quadrics in order to obtain generic curvature loci of regular $3$-manifolds in $\mathbb{R}^6$ and singular corank $1$ $3$-manifolds in $\mathbb{R}^5$. For this, we characterize the type of the curva
Externí odkaz:
http://arxiv.org/abs/2204.12312
For singular $n$-manifolds in $\mathbb R^{n+k}$ with a corank 1 singular point at $p\in M^n_{\mbox{sing}}$ we define up to $l(n-1)$ different axial curvatures at $p$, where $l=\min\{n,k+1\}$. These curvatures are obtained using the curvature locus (t
Externí odkaz:
http://arxiv.org/abs/2204.06606
We study the geometry of surfaces in $\mathbb R^5$ by relating it to the geometry of regular and singular surfaces in $\mathbb R^4$ obtained by orthogonal projections. In particular, we obtain relations between asymptotic directions, which are not se
Externí odkaz:
http://arxiv.org/abs/2010.10976
Autor:
Sinha, Raúl Oset, Saji, Kentaro
For singular corank 1 surfaces in $\mathbb R^3$ we introduce a distinguished normal vector called the axial vector. Using this vector and the curvature parabola we define a new type of curvature called the axial curvature, which generalizes the singu
Externí odkaz:
http://arxiv.org/abs/1911.08823
Autor:
Riul, Pedro Benedini, Sinha, Raúl Oset
We use normal sections to relate the curvature locus of regular (resp. singular corank 1) 3-manifolds in $\mathbb{R}^6$ (resp. $\mathbb R^5$) with regular (resp. singular corank 1) surfaces in $\mathbb R^5$ (resp. $\mathbb R^4$). For example we show
Externí odkaz:
http://arxiv.org/abs/1909.07307
Autor:
Riul, Pedro Benedini, Sinha, Raúl Oset
We study the flat geometry of the least degenerate singularity of a singular surface in $\mathbb R^4$, the $I_{1}$ singularity parametrised by $(x,y)\mapsto(x,xy,y^{2},y^{3})$. This singularity appears generically when projecting a regular surface in
Externí odkaz:
http://arxiv.org/abs/1804.11220
We define the extra-nice dimensions and prove that the subset of locally stable 1-parameter families in $C^{\infty}(N\times[0,1],P)$, also known as pseudo-isotopies, is dense if and only if the pair of dimensions $(\dim N, \dim P)$ is in the extra-ni
Externí odkaz:
http://arxiv.org/abs/1804.09414
We study the geometry of surfaces in $\mathbb{R}^{4}$ with corank $1$ singularities. For such surfaces the singularities are isolated and at each point we define the curvature parabola in the normal space. This curve codifies all the second order inf
Externí odkaz:
http://arxiv.org/abs/1801.06380