Results 1 to 10 of about 220,392 (138)
Non-embeddable Real Algebraic Hypersurfaces [PDF]
Mathematische Zeitschrift (2013) 275:657-671, 2013 We study various classes of real hypersurfaces that are not embeddable into more special hypersurfaces in higher dimension, such as spheres, real algebraic compact strongly pseudoconvex hypersurfaces or compact pseudoconvex hypersurfaces of finite type. We conclude by stating some open problems.
Dmitri Zaitsev, Xiaojun Huang
arxiv +8 more sources
On real forms of Fermat hypersurfaces [PDF]
arXiv, 2023 In this paper, we compute the number of real forms of Fermat hypersurfaces for degree $d \ge 3$ except the degree 4 surface case, and give explicit descriptions of them.
arxiv +3 more sources
Hopf hypersurfaces in spaces of oriented geodesics [PDF]
J. Geom. 108 (2017) 1129 -1135, 2016 A Hopf hypersurface in a (para-)Kaehler manifold is a real hypersurface for which one of the principal directions of the second fundamental form is the (para-)complex dual of the normal vector. We consider particular Hopf hypersurfaces in the space of oriented geodesics of a non-flat space form of dimension greater than 2.
arxiv +1 more source
Hopf hypersurfaces in complex Grassmannians of rank two [PDF]
, 2015 In this paper, we study real hypersurfaces in complex Grassmannians of rank two. First, the nonexistence of mixed foliate real hypersurfaces is proven. With this result, we show that for Hopf hypersurfaces in complex Grassmannians of rank two, the Reeb principal curvature is constant along integral curves of the Reeb vector field.
arxiv +1 more source
Tangential real hypersurfaces on Hermite-like manifolds [PDF]
arXiv, 2022 Non-degenerate real hypersurfaces of almost Hermite-like manifolds are examined. Tangential real hypersurfaces are introduced and the main identities of such hypersurfaces are obtained. With the help of these identities, contact metric structures of certain kinds, namely K-contact and cosymplectic cases, are discussed.
arxiv
$\mathfrak A$-principal Hopf hypersurfaces in complex quadrics [PDF]
, 2017 A real hypersurface in the complex quadric $Q^m=SO_{m+2}/SO_mSO_2$ is said to be $\mathfrak A$-principal if its unit normal vector field is singular of type $\mathfrak A$-principal everywhere. In this paper, we show that a $\mathfrak A$-principal Hopf hypersurface in $Q^m$, $m\geq3$ is an open part of a tube around a totally geodesic $Q^{m+1}$ in $Q^m$.
arxiv +1 more source
Holomorphic extension of meromorphic mappings along real analytic hypersurfaces [PDF]
Ann. Mat. Pura Appl. (2020), 2019 Let $M\subset \mathbb C^n$ be a real analytic hypersurface, $M'\subset \mathbb C^N$ $(N\geq n)$ be a strongly pseudoconvex real algebraic hypersurface of the special form and $F$ be a meromorphic mapping in a neighborhood of a point $p\in M$ which is holomorphic in one side of $M$.
arxiv +1 more source
Nullity distributions on real hypersurfaces in non-flat complex space forms [PDF]
arXiv, 2016 In this paper the result of real hypersurfaces in non-flat complex space forms, whose structure vector field $\xi$ belongs to the $\kappa$-nullity distribution is extended in case of three dimensional real hypersurfaces in non-flat complex space forms.
arxiv
Existence of real algebraic hypersurfaces with many prescribed components [PDF]
arXiv, 2022 Given a real algebraic variety $X$ of dimension $n$, a very ample divisor $D$ on $X$ and a smooth closed hypersurface $\Sigma$ of $\mathbf{R}^n$, we construct real algebraic hypersurfaces in the linear system $|mD|$ whose real locus contains many connected components diffeomorphic to $\Sigma$.
arxiv
Curvature properties of Lie hypersurfaces in the complex hyperbolic space [PDF]
arXiv, 2009 A Lie hypersurface in the complex hyperbolic space is a homogeneous real hypersurface without focal submanifolds. The set of all Lie hypersurfaces in the complex hyperbolic space is bijective to a closed interval, which gives a deformation of homogeneous hypersurfaces from the ruled minimal one to the horosphere.
arxiv