Classification Of Real Hypersurfaces Research Articles

Local description of homogeneous real hypersurfaces of the two-dimensional complex space in terms of their normal equations

In the paper, a classification of real hypersurfaces of the space ℂ2 that admit transitive actions of local Lie groups of holomorphic transformations is constructed.

On real hypersurfaces in quaternionic projective space with 𝒟⊥‐recurrent second fundamental tensor

In this paper, we give a complete classification of real hypersurfaces in a quaternionic projective space QPm with 𝒟⊥‐recurrent second fundamental tensor under certain condition on the orthogonal distribution 𝒟.

Ricci Tensors of Real Hypersurfaces in a Complex Projective Space

This paper gives a classification of real hypersurfaces in a complex projective space under assumptions that the structure vector $\xi$ is principal, the focal map has constant rank, and ${\nabla _\xi }S = 0$, where S is the Ricci tensor of the real hypersurface.

Ricci tensors of real hypersurfaces in a complex projective space

This paper gives a classification of real hypersurfaces in a complex projective space under assumptions that the structure vector ξ \xi is principal, the focal map has constant rank, and ∇ ξ S = 0 {\nabla _\xi }S = 0 , where S is the Ricci tensor of the real hypersurface.

A Kernel Approach to the Local Solvability of the Tangential Cauchy Riemann Equations

An integral kernel approach is given for the proof of the theorem of Andreotti and Hill which states that the $Y(q)$ condition of Kohn is a sufficient condition for local solvability of the tangential Cauchy Riemann equations on a real hypersurface in ${{\mathbf {C}}^n}$. In addition, we provide an integral kernel approach to nonsolvability for a certain class of real hypersurfaces in the case when $Y(q)$ is not satisfied.

A kernel approach to the local solvability of the tangential Cauchy Riemann equations

An integral kernel approach is given for the proof of the theorem of Andreotti and Hill which states that the Y ( q ) Y(q) condition of Kohn is a sufficient condition for local solvability of the tangential Cauchy Riemann equations on a real hypersurface in C n {{\mathbf {C}}^n} . In addition, we provide an integral kernel approach to nonsolvability for a certain class of real hypersurfaces in the case when Y ( q ) Y(q) is not satisfied.