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Hypersurfaces

Xem 1-20 trên 24 kết quả Hypersurfaces
  • The interplay between geometry and topology on complex algebraic varieties is a classical theme that goes back to Lefschetz [L] and Zariski [Z] and is always present on the scene; see for instance the work by Libgober [Li]. In this paper we study complements of hypersurfaces, with special attention to the case of hyperplane arrangements as discussed in Orlik-Terao’s book [OT1]. Theorem 1 expresses the degree of the gradient map associated to any homogeneous polynomial h as the number of n-cells that have to be added to a generic hyperplane section D(h) ∩ H to obtain the complement in...

    pdf36p tuanloccuoi 04-01-2013 124 5   Download

  • Let M be an isoparametric hypersurface in the sphere S n with four distinct principal curvatures. M¨nzner showed that the four principal curvatures can u have at most two distinct multiplicities m1 , m2 , and Stolz showed that the pair (m1 , m2 ) must either be (2, 2), (4, 5), or be equal to the multiplicities of an isoparametric hypersurface of FKM-type, constructed by Ferus, Karcher and M¨nzner from orthogonal representations of Clifford algebras. In this paper, u we prove that if the multiplicities satisfy m2 ≥ 2m1 − 1, then the isoparametric hypersurface M must be...

    pdf77p noel_noel 17-01-2013 37 5   Download

  • The aim of this paper is to show that the preservation of irreducibility of sections between a variety and hypersurface by specializations and almost all sections between a linear subspace of dimension h = n − d of Pn and a nondegenerate variety k of dimension d 0 consists of s points in uniform position. Introduction The lemma of Haaris [2] about a set in the uniform position has attracted much attention in algebraic geometry. That is a set of points of a projective space such that any two subsets of them with the same cardinality have the same...

    pdf9p tuanlocmuido 19-12-2012 34 2   Download

  • This paper deals with the relative nullity distributions of lightlike hypersurfaces of indefinite Kenmotsu space forms, tangent to the structure vector field. Theorems on parallel vector fields are obtained. We give characterization theorems for the relative nullity distributions as well as for Einstein, totally contact umbilical and flat lightlike hypersurfaces.

    pdf21p tuongvidanh 06-01-2019 15 0   Download

  • We mainly deal with the problem of admissibility for screen distributions on a lightlike hypersurface of both a semi-Riemannian manifold and an indefinite S -manifold. In the latter case, we first show that a characteristic screen distribution is never admissible, and then we provide a characterization for admissible screen distributions on proper totally umbilical lightlike hypersurfaces.

    pdf13p tuongvidanh 06-01-2019 12 0   Download

  • We study lightlike hypersurfaces of a semi-Riemannian manifold satisfying pseudosymmetry conditions. We give sufficient conditions for a lightlike hypersurface to be pseudosymmetric and show that there is a close relationship of the pseudosymmetry condition of a lightlike hypersurface and its integrable screen distribution.

    pdf21p danhdanh27 07-01-2019 8 0   Download

  • We prove the non-existence of Hopf real hypersurfaces in complex two-plane Grassmannians whose shape operator A is generalized Tanaka–Webster recurrent if the principal curvature of the structure vector field is not equal to trace(A).

    pdf9p danhdanh27 07-01-2019 7 0   Download

  • We define the notion of a metallic shaped hypersurface and give the full classification of metallic shaped hypersurfaces in real space forms. We deduce that every metallic shaped hypersurface in real space forms is a semisymmetric hypersurface.

    pdf11p danhdanh27 07-01-2019 10 0   Download

  • In this paper, we investigate lightlike hypersurfaces which are semi-symmetric, Ricci semi-symmetric, parallel or semi-parallel in a semi-Euclidean space. We obtain that every screen conformal lightlike hypersurface of the Minkowski spacetime is semi-symmetric.

    pdf24p danhdanh27 07-01-2019 11 0   Download

  • In this paper, lightlike hypersurfaces of indefinite Kenmotsu space form are studied. Some characterizations of non-existence of lightlike hypersurfaces of indefinite Kenmotsu space form are given.

    pdf13p danhdanh27 07-01-2019 6 0   Download

  • In this article, we prove a uniqueness theorem for algebraically non-degenerate holomorphic curves on annulus sharing hypersurfaces in general position for Veronese embedding.

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  • The purpose of this article is to show that there exists a smooth real hypersurface germ (M p), of D'Angelo infinite type in C2 such that it does not admit any (singular) holomorphic curve that has infinite order contact with M at p .

    pdf6p viposeidon2711 17-09-2019 10 0   Download

  • In this paper, we establish a second main theorem with a good defect relation for entire curves in a projective variety whose derivatives vanish on inverse image of hypersurface targets. Our method is a combination of the techniques in [7-9].

    pdf10p koxih_kothogmih5 04-09-2020 5 0   Download

  • In this paper we give a new proof for the classification result in [3]. We show that isoparametric hypersurfaces with four distinct principal curvatures in spheres are of Clifford type provided that the multiplicities m1 , m2 of the principal curvatures satisfy m2 ≥ 2m1 − 1. This inequality is satisfied for all but five possible pairs (m1 , m2 ) with m1 ≤ m2 .

    pdf15p dontetvui 17-01-2013 56 6   Download

  • In 1926, R. Nevanlinna [6] showed that for two nonconstant meromorphic functions f and g on the complex plane C , if they have the same inverse images for five distinct values then f=g. In 1975, H. Fujimoto [4] generalized the above result to the case of meromorphic mappings of m C into n.

    pdf4p cumeo2006 02-07-2018 11 1   Download

  • In this paper, by applying the generalized Omori–Yau maximum principle for complete spacelike hypersurfaces in warped product spaces, we obtain the sign relationship between the derivative of warping function and support function.

    pdf12p danhdanh27 07-01-2019 4 0   Download

  • Classical differential geometry is the approach to geometry that takes full advantage of the introduction of numerical coordinates into a geometric space. This use of coordinates in geometry was the essential insight of Rene Descartes that allowed the invention of analytic geometry and paved the way for modern differential geometry. The basic object in differential geometry (and differential topology) is the smooth manifold. This is a topological space on which a sufficiently nice family of coordinate systems or "charts" is defined.

    pdf0p taurus23 26-09-2012 71 9   Download

  • We prove Maruyama’s conjecture on the boundedness of slope semistable sheaves on a projective variety defined over a noetherian ring. Our approach also gives a new proof of the boundedness for varieties defined over a characteristic zero field. This result implies that in mixed characteristic the moduli spaces of Gieseker semistable sheaves are projective schemes of finite type. The proof uses a new inequality bounding slopes of the restriction of a sheaf to a hypersurface in terms of its slope and the discriminant.

    pdf27p tuanloccuoi 04-01-2013 44 6   Download

  • Let X be a smooth quasiprojective subscheme of Pn of dimension m ≥ 0 over Fq . Then there exist homogeneous polynomials f over Fq for which the intersection of X and the hypersurface f = 0 is smooth. In fact, the set of such f has a positive density, equal to ζX (m + 1)−1 , where ζX (s) = ZX (q −s ) is the zeta function of X. An analogue for regular quasiprojective schemes over Z is proved, assuming the abc conjecture and another conjecture. 1. Introduction The classical Bertini theorems say that if a subscheme...

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  • In this paper, we develop an approach for establishing in some important cases, a conjecture made by De Giorgi more than 20 years ago. The problem originates in the theory of phase transition and is so closely connected to the theory of minimal hypersurfaces that it is sometimes referred to as “the version of Bernstein’s problem for minimal graphs”. The conjecture has been completely settled in dimension 2 by the authors [15] and in dimension 3 in [2], yet the approach in this paper seems to be the first to use, in an essential way, the solution of...

    pdf23p tuanloccuoi 04-01-2013 53 4   Download

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