The Experts below are selected from a list of 14655 Experts worldwide ranked by ideXlab platform
Philippe Ellia - One of the best experts on this subject based on the ideXlab platform.
-
Double Structures and Normal Bundle of Space Curves
Journal of the London Mathematical Society, 1998Co-Authors: Philippe ElliaAbstract:It is shown that the general plane section of a double structure on an integral curve C ⊆ P 3 has a connected numerical character (that is, its Hilbert function is of decreasing type). The paper gives applications, particularly to the stability of the Normal Bundle of space curves.
Ruy Tojeiro - One of the best experts on this subject based on the ideXlab platform.
-
submanifolds with nonparallel first Normal Bundle revisited
arXiv: Differential Geometry, 2011Co-Authors: Marcos Dajczer, Ruy TojeiroAbstract:In this paper, we analyze the geometric structure of an Euclidean submanifold whose osculating spaces form a nonconstant family of proper subspaces of the same dimension. We prove that if the rate of change of the osculating spaces is small, then the submanifold must be a (submanifold of a) ruled submanifold of a very special type. We also give a sharp estimate of the dimension of the rulings.
-
pseudo parallel submanifolds with flat Normal Bundle of space forms
Glasgow Mathematical Journal, 2006Co-Authors: G. A. Lobos, Ruy TojeiroAbstract:We provide a complete local classification of pseudoparallel submanifolds with flat Normal Bundle of space forms, extending the classification by Dillen-Nolker for the semi-parallel case.
-
Submanifolds with nonparallel first Normal Bundle
Canadian Mathematical Bulletin, 1994Co-Authors: Marcos Dajczer, Ruy TojeiroAbstract:AbstractWe provide a complete local geometric description of submanifolds of spaces with constant sectional curvature where the first Normal spaces, that is, the subspaces spanned by the second fundamental form, form a vector subBundle of the Normal Bundle of low rank which is nonparallel in the Normal connection. We also characterize flat submanifolds with flat Normal Bundle in Euclidean space satisfying the helix property.
Hezi Lin - One of the best experts on this subject based on the ideXlab platform.
-
On the Structure of Submanifolds in Euclidean Space with Flat Normal Bundle
Results in Mathematics, 2015Co-Authors: Hezi LinAbstract:In this paper we study the structure of an immersed submanifold M n in a Riemannian manifold with flat Normal Bundle in two ways. Firstly, we prove that if M n is compact and satisfies some pointwise pinching condition, and assume further that the ambient space has pure curvature tensor and non-negative isotropic curvature, then the Betti numbers β p (M) = 0 for 2 ≤ p ≤ n−2. Secondly, suppose that M n is a complete non-compact submanifold in the Euclidean space with finite total curvature in the sense that its traceless second fundament form has finite L n -norm, then we show that the spaces of L 2 harmonic p-forms on M n have finite dimensions for all 2 ≤ p ≤ n−2.
Olivier Thom - One of the best experts on this subject based on the ideXlab platform.
-
On the formal principle for curves on projective surfaces
Mathematische Annalen, 2020Co-Authors: Jorge Vitório Pereira, Olivier ThomAbstract:We prove that the formal completion of a complex projective surface along a rigid smooth curve with trivial Normal Bundle determines the birational equivalence class of the surface.
-
Formal classication of two-dimensional neighborhoods of genus g ≥ 2 curves with trivial Normal Bundle
arXiv: Algebraic Geometry, 2018Co-Authors: Olivier ThomAbstract:In this paper we study the formal classication of two-dimensional neighborhoods of genus g ≥ 2 curves with trivial Normal Bundle. We first construct formal foliations on such neighborhoods with holonomy vanishing along many loops, then give the formal/analytic classication of neighborhoods equipped with two foliations, and finally put this together to obtain a description of the space of neighborhoods up to formal equivalence.
-
formal classication of two dimensional neighborhoods of genus g 2 curves with trivial Normal Bundle
arXiv: Algebraic Geometry, 2018Co-Authors: Olivier ThomAbstract:In this paper we study the formal classication of two-dimensional neighborhoods of genus g ≥ 2 curves with trivial Normal Bundle. We first construct formal foliations on such neighborhoods with holonomy vanishing along many loops, then give the formal/analytic classication of neighborhoods equipped with two foliations, and finally put this together to obtain a description of the space of neighborhoods up to formal equivalence.
Alberto Alzati - One of the best experts on this subject based on the ideXlab platform.
-
Remarks on the Normal Bundles of generic rational curves
ANNALI DELL'UNIVERSITA' DI FERRARA, 2017Co-Authors: Alberto AlzatiAbstract:In this note we give a different proof of Sacchiero’s theorem about the splitting type of the Normal Bundle of a generic rational curve. Moreover we discuss the existence and the construction of smooth monomial curves having generic type of the Normal Bundle.
-
An algorithm for the Normal Bundle of rational monomial curves
Rendiconti del Circolo Matematico di Palermo Series 2, 2017Co-Authors: Alberto Alzati, Alfonso TortoraAbstract:We give a method to calculate the cohomology of the twisted Normal Bundle over a smoth rational curve. From this method we derive a vanishing result and an algorithm for calculating the splitting type of the Bundle for any rational monomial curve.
-
An algorithm for the Normal Bundle of rational monomial curves
arXiv: Algebraic Geometry, 2015Co-Authors: Alberto Alzati, Alfonso TortoraAbstract:We give an algorithm for calculating the splitting type of the Normal Bundle of any rational monomial curve. The algorithm is obtained by reducing the calculus to a combinatorial problem and then by solving this problem.
-
Irreducible Components of Hilbert Schemes of Rational Curves with given Normal Bundle
arXiv: Algebraic Geometry, 2015Co-Authors: Alberto AlzatiAbstract:We develop a new general method for computing the decomposition type of the Normal Bundle to a projective rational curve. This method is then used to detect and explain an example of a Hilbert scheme that parametrizes all the rational curves in $\mathbb{P}^s$ with a given decomposition type of the Normal Bundle and that has exactly two irreducible components. This gives a negative answer to the very old question whether such Hilbert schemes are always irreducible. We also characterize smooth non-degenerate rational curves contained in rational Normal scroll surfaces in terms of the splitting type of their restricted tangent Bundles, compute their Normal Bundles and show how to construct these curves as suitable projections of a rational Normal curve.
