Polynomials with constant Hessian determinant
نویسندگان
چکیده
منابع مشابه
Polynomials with constant Hessian determinants in dimension three
In this paper, we show that the Jacobian conjecture holds for gradient maps in dimension n ≤ 3 over a field K of characteristic zero. We do this by extending the following result for n ≤ 2 by F. Dillen to n ≤ 3: if f is a polynomial of degree larger than two in n ≤ 3 variables such that the Hessian determinant of f is constant, then after a suitable linear transformation (replacing f by f(Tx) f...
متن کاملintegral inequalities for submanifolds of hessian manifolds with constant hessian sectional curvature
in this paper, we obtain two intrinsic integral inequalities of hessian manifolds.
متن کاملHessian Nilpotent Polynomials and the Jacobian Conjecture
Let z = (z1, · · · , zn) and ∆ = ∑n i=1 ∂ 2 ∂z i the Laplace operator. The main goal of the paper is to show that the wellknown Jacobian conjecture without any additional conditions is equivalent to the following what we call vanishing conjecture: for any homogeneous polynomial P (z) of degree d = 4, if ∆P(z) = 0 for all m ≥ 1, then ∆P(z) = 0 when m >> 0, or equivalently, ∆P(z) = 0 when m > 3 2...
متن کاملOn the Complex and Real Hessian Polynomials
A topic which has been of interest since the XIX century is the study of the parabolic curve of smooth surfaces in real three-dimensional space, as shown in the works of Gauss, Darboux, Salmon 1 , Kergosien and Thom 2 , Arnold 3 , among others. The parabolic curve of the graph of a smooth function, f : R2 → R, is the set { p, f p ∈ R2 × R: Hessf p 0}, where Hess f : fxxfyy − f2 xy. In this case...
متن کاملTwo Results on Homogeneous Hessian Nilpotent Polynomials
Let z = (z1, · · · , zn) and ∆ = ∑n i=1 ∂ 2 ∂z i the Laplace operator. A formal power series P (z) is said to be Hessian Nilpotent(HN) if its Hessian matrix HesP (z) = ( ∂ 2 P ∂zi∂zj ) is nilpotent. In recent developments in [BE1], [M] and [Z], the Jacobian conjecture has been reduced to the following so-called vanishing conjecture(VC) of HN polynomials: for any homogeneous HN polynomial P (z) ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1991
ISSN: 0022-4049
DOI: 10.1016/0022-4049(91)90037-3