biharmonic surfaces in euclidean space $mathbb{e}^3$ are firstly studied from a differential geometric point of view by bang-yen chen, who showed that the only biharmonic surfaces are minimal ones. a surface $x : m^2rightarrowmathbb{e}^{3}$ is called biharmonic if $delta^2x=0$, where $delta$ is the laplace operator of $m^2$. we study the $l_k$-biharmonic spacelike hypersurfaces in the $4$-dimen...

We show that the base spaces of semiuniversal unfoldings some weighted homogeneous singularities can be identified with moduli A ∞ $A_\infty$ -structures on trivial extension algebras endomorphism tilting objects. The same also appear in Fukaya categories their mirrors. Based these identifications, we discuss applications to homological mirror symmetry for Milnor fibers, and give a proof an n $...

In this paper, we study n(n ≥ 3)-dimensional complete connected and oriented space-like hypersurfaces Mn in an (n+1)-dimensional Lorentzian space form Mn+1 1 (c) with non-zero constant k-th (k < n) mean curvature and two distinct principal curvatures λ and μ. We give some characterizations of Riemannian product H(c1) ×Mn−m(c2) and show that the Riemannian product Hm(c1)×Mn−m(c2) is the only com...

We describe methods for computing an implicit model of a hypersurface that is given only by a finite sampling. The methods work by mapping the sample points into a reproducing kernel Hilbert space and then determining regions in terms of hyperplanes.

Let Y be a hypersurface in a 2n-dimensional holomorphic symplectic manifold X. The restriction σ|Y of the holomorphic symplectic form induces a rank one foliation on Y . We investigate situations where this foliation has compact leaves; in such cases we obtain a space of leaves Y/F which has dimension 2n − 2 and admits a holomorphic symplectic form.

— In the moduli space Pd of degree d polynomials, the set Pern(w) of classes [f ] for which f admits a cycle of exact period n and multiplier multiplier w is known to be an algebraic hypersurface. We prove that, given w ∈ C, these hypersurfaces equidistribute towards the bifurcation current as n tends to infinity.

A problem naturally arizing in the unit-cost complexity class NP over the field of complex numbers consists in deciding if an input of length 2n belongs to a special absolutely irreducible hypersurface of the affine space 2n . Consequently, the decision problem is substituted by a computation problem.

In this paper, we study the geometry of lightlike hypersurfaces of an indefinite trans-Sasakian manifold with a quarter-symmetric metric connection. The main result is a characterization theorem for such a lightlike hypersurface of an indefinite generalized Sasakian space form. Mathematics Subject Classification: 53C25, 53C40, 53C50

We study a one-to-one map between massless scalar fields on d+1 dimensional Minkowski (Euclidean) space time and scalar fields on d+1 dimensional De Sitter (Euclidean AdS) space. We solve the Klein-Gordon equation for massless scalar field in terms of initial data on the hypersurface t=0 which is isomorphic to the boundary of dS (AdS) space. By inserting these solutions into the action of massl...

The causal boundary of string propagation – defined as the hypersurface in loop space bordering the timelike(spacelike) domains in which two successive measurements of the string field do(do not) interfere with one another – is argued to be 0 = dσ δX(σ) 2 = ∞ ℓ=−∞ δx µ −ℓ δx µ ℓ. Some possible consequences are discussed.