A real n-dimensional homogeneous polynomial f (x) of degree m and a real constant c define an algebraic hypersurface S whose points satisfy f (x) = c. The polynomial f can be represented by Axm where A is a real mth order n-dimensional supersymmetric tensor. In this paper, we define rank, base index and eigenvalues for the polynomial f , the hypersurface S and the tensor A. The rank is a nonneg...

We study pseudoholomorphic discs with boundaries attached to a real hypersurface E in an almost complex manifold of dimension 2. We prove that if E contains no discs, then they fill a one sided neighborhood of E. MSC: 32H02, 53C15.

We study Levi-flat real analytic hypersurfaces with singularities. We prove that the Levi foliation on the regular part of the hypersurface can be holomorphically extended, in a suitable sense, to neighbourhoods of singular

It is shown that there exist real analytic real hypersurfaces in C" which cannot be locally holomorphically imbedded in any finite dimensional sphere S2N~l cCM. In [1], Chern and Moser developed a theory of local invariants of real hypersurfaces in complex manifolds. In doing so, they stressed the analogies between pseudoconformal geometry and Riemannian geometry, defining analogues of the Riem...

Proof. First consider the following example of the Conner-Floyd theorem. Let H,,,,,(C) denote a non-singular hypersurface of degree (1,l) in the product P,,,(C) x P.(C). b terms of homogeneous co-ordinates (wO, . . . , w,) and (z,,, . . . , .z”) with m 5 n this hypersurface can be defined as the locus w,,z, + wlzl + . . . + w,,,z, = 0. It can also be thought of as a P,_,(C)-bundle over P,(C).] ...

We give series of explicit examples of Levi-nondegenerate real-analytic hypersurfaces in complex spaces that are not transversally holomorphically embeddable into hyperquadrics of any dimension. For this, we construct invariants attached to a given hypersurface that serve as obstructions to embeddability. We further study the embeddability problem for real-analytic submanifolds of higher codime...

Let M be a real hypersurface of complex space form n ( c ) $M^n(c)$ , ≠ 0 $c\ne 0$ . Suppose that the structure vector field ξ is an eigen Ricci tensor S, S = β $S\xi =\beta \xi$ being function. We study on M, gradient pseudo-Ricci soliton g f λ μ $M,g,f,\lambda ,\mu$ extended concept soliton, closely related to pseudo-Einstein hypersurfaces. When ≥ 3 $n\ge 3$ we show Hopf hypersurface.

The objective of this paper is to show how the recently proposed method by Giusti, Heintz, Morais, Morgenstern, Pardo 10] can be applied to a case of real polynomial equation solving. Our main result concerns the problem of nding one representative point for each connected component of a real bounded smooth hypersurface. The algorithm in 10] yields a method for symbolically solving a zero-dimen...

Abstract. The hypersurface amoeba membership problem is the problem to decide whether for an input point λ ∈ R, the point λ is an element of the amoeba of the hypersurface generated by a multivariate complex Laurent polynomial c. We present an algorithm to solve this problem based on semidefinite programming and on Lasserre’s moment method for approximating the minimum of a real polynomial. The...