Results 41 to 50 of about 72,858 (181)
Differential Geometry and Matrix-Based Generalizations of the Pythagorean Theorem in Space Forms
MathematicsIn this work, we consider Pythagorean triples and quadruples using fundamental form matrices of hypersurfaces in three- and four-dimensional space forms and illustrate various figures. Moreover, we generalize that an immersed hypersphere Mn with radius r
Erhan Güler +2 more
doaj +1 more source
On the equivalence of two curvature conditions for Lorentzian hypersurfaces
Arab Journal of Mathematical Sciences, 2017 Let n≥3. We show that semi-symmetry and Ricci-semisymmetry conditions are equivalent for any n-dimensional Lorentzian hypersurface in a Lorentzian space form with nonzero curvature.
Mohammed Guediri, Norah Alshehri
doaj +1 more source
Generic hypersurface singularities
Proceedings - Mathematical Sciences, 1997 We give a new differential proof of our result on the maximal rank of generic unions of points of multiplicity two in projective space in degrees greater than five. This simplifies somewhat our proof of the Waring conjecture.
Alexander, James, Hirschowitz, André
openaire +3 more sources
On computing local monodromy and the numerical local irreducible decomposition
Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.Abstract Similarly to the global case, the local structure of a holomorphic subvariety at a given point is described by its local irreducible decomposition. Geometrically, the key requirement for obtaining a local irreducible decomposition is to compute the local monodromy action of a generic linear projection at the given point, which is always well ...
Parker B. Edwards +1 more
wiley +1 more source
On the backward stability of the Schwarzschild black hole singularity
, 2015 We study the backwards-in-time stability of the Schwarzschild singularity from a dynamical PDE point of view. More precisely, considering a spacelike hypersurface $\Sigma_0$ in the interior of the black hole region, tangent to the singular hypersurface $\
Fournodavlos, Grigorios
core +1 more source
Nonrational Weighted Hypersurfaces [PDF]
Nagoya Mathematical Journal, 2009 AbstractThe aim of this paper is to construct (i) infinitely many families of nonrational ℚ-Fano varieties of arbitrary dimension ≥ 4 with at most quotient singularities, and (ii) twelve families of nonrational ℚ-Fano threefolds with at most terminal singularities among which two are new and the remaining ten give an alternate proof of nonrationality ...
openaire +3 more sources
Rational points on even‐dimensional Fermat cubics
Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.Abstract We show that even‐dimensional Fermat cubic hypersurfaces are rational over any field of characteristic not equal to three, by constructing explicit rational parameterizations with polynomials of low degree. As a byproduct of our rationality constructions, we obtain estimates for the number of their rational points over a number field and ...
Alex Massarenti
wiley +1 more source
Bernstein-type theorems in hypersurfaces with constant mean curvature
Anais da Academia Brasileira de Ciências, 2000 By using the nodal domains of some natural function arising in the study of hypersurfaces with constant mean curvature we obtain some Bernstein-type theorems.
MANFREDO P. DO CARMO, DETANG ZHOU
doaj +1 more source
On a property of W4 -manifolds
Дифференциальная геометрия многообразий фигур, 2020 The properties of almost Hermitian manifolds belonging to the Gray — Hervella class W4 are considered. The almost Hermitian manifolds of this class were studied by such outstanding geometers like Alfred Gray, Izu Vaisman, and Vadim Feodorovich Kirichenko.
M.B. Banaru
doaj +1 more source
Parallel umbilical hypersurfaces [PDF]
Proceedings of the American Mathematical Society, 1965 The only umbilical surfaces of Euclidean space are planes and spheres. We propose to study umbilical hypersurfaces in Riemannian space with the added condition that they constitute a system of parallels. As will be shown, such families only exist in spaces of constant curvature.
openaire +1 more source