7 citations · 20 across the 17 of their papers we have counts for
20 papers
Bi-Lipschitz triviality of function-germs on singular varieties
Raúl Oset Sinha, Maria Aparecida Soares Ruas
In this paper we study the bi-Lipschitz triviality of deformations of an analytic function germ defined on a germ of an analytic variety in . We introduce…
A proof of the Mond conjecture for wave fronts
C. Muñoz-Cabello, J. J. Nuño-Ballesteros, R. Oset Sinha
We prove the Mond conjecture for wave fronts which states that the number of parameters of a frontal versal unfolding is less than or equal to the number of spheres in the image of…
Augmentation of singularities: -type conjectures and simplicity
Ignacio Breva Ribes, Raúl Oset Sinha
For function germs it is well known that and it has recently been proved by Liu that . We giv…
Deformations of corank frontals
C. Muñoz-Cabello, J. J. Nuño-Ballesteros, R. Oset Sinha
We develop a Thom-Mather theory of frontals analogous to Ishikawa's theory of deformations of Legendrian singularities but at the frontal level, avoiding the use of the contact set…
Axial curvatures for corank 1 singular -manifolds in
Pedro Benedini Riul, Jorge Luiz Deolindo Silva, Raúl Oset Sinha
For singular -manifolds in with a corank 1 singular point at $p\in M^n_{\mbox{sing}}$ we define up to different axial curvatures at , where $l=\min…
Simplicity of augmentations of codimension 1 germs and by Morse functions
I. Breva Ribes, R. Oset Sinha
We study the simplicity of map-germs obtained by the operation of augmentation and describe how to obtain their versal unfoldings. When the augmentation comes from an $\mathscr{A}_…
Geometry of surfaces in through projections and normal sections
Jorge Deolindo Silva, Raúl Oset Sinha
We study the geometry of surfaces in by relating it to the geometry of regular and singular surfaces in obtained by orthogonal projections. In particula…
The axial curvature for corank 1 singular surfaces
Raúl Oset Sinha, Kentaro Saji
For singular corank 1 surfaces in we introduce a distinguished normal vector called the axial vector. Using this vector and the curvature parabola we define a new typ…
Relating second order geometry of manifolds through projections and normal sections
Pedro Benedini Riul, Raúl Oset Sinha
We use normal sections to relate the curvature locus of regular (resp. singular corank 1) 3-manifolds in (resp. ) with regular (resp. singular corank 1)…
The flat geometry of the singularity:
Pedro Benedini Riul, Raúl Oset Sinha
We study the flat geometry of the least degenerate singularity of a singular surface in , the singularity parametrised by . Thi…
The extra-nice dimensions
Raúl Oset Sinha, Maria Aparecida Soares Ruas, Roberta Wik Atique
We define the extra-nice dimensions and prove that the subset of locally stable 1-parameter families in , also known as pseudo-isotopies, is dense if an…
The geometry of corank surfaces in
Pedro Benedini Riul, Raúl Oset Sinha, Maria Aparecida Soares Ruas
We study the geometry of surfaces in with corank singularities. For such surfaces the singularities are isolated and at each point we define the curvature para…
A relation between the curvature ellipse and the curvature parabola
Raúl Oset Sinha, Pedro Benedini Riul
At each point in an immersed surface in there is a curvature ellipse in the normal plane which codifies all the local second order geometry of the surface. More recen…
On the flat geometry of the cuspidal edge
Raúl Oset Sinha, Farid Tari
We study the geometry of the cuspidal edge in derived from its contact with planes and lines (referred to as flat geometry). The contact of with planes is mea…
Liftable vector fields, unfoldings and augmentations
Juan José Nuño Ballesteros, Raúl Oset Sinha
We study liftable vector fields of smooth map-germs. We show how to obtain the module of liftable vector fields of any map-germ of finite singularity type from the module of liftab…
First order local invariants of planar caustics
Raúl Oset Sinha, María del Carmen Romero Fuster
We study first order local invariants of Vassiliev type for Lagrangian immersions with generic planar caustics. For this we produce some examples of 2-parameter families of Lagrang…
On the simplicity of multigerms
Raúl Oset Sinha, Maria Aparecida Soares Ruas, Roberta Wik Atique
We prove several results regarding the simplicity of germs and multigerms obtained via the operations of augmentation, simultaneous augmentation and concatenation and generalised c…
Liftable vector fields over corank one multigerms
T. Nishimura, R. Oset Sinha, M. A. S. Ruas +1
In this paper, a systematic method is given to construct all liftable vector fields over an analytic multigerm of corank at most one admi…
Classifying codimension 2 multigerms
R. Oset Sinha, M. A. S. Ruas, R. Wik Atique
We generalise the operations of augmentation and concatenations in order to obtain multigerms of analytic (or smooth) maps with $\mathbb…
Generalized distance-squared mappings of the plane into the plane
S. Ichiki, T. Nishimura, R. Oset Sinha +1
We define generalized distance-squared mappings, and we concentrate on the plane to plane case. We classify generalized distance-squared mappings of the plane into the plane in a r…