相关论文: Semi-parallel real hypersurfaces in complex two-pl…
It is known that a surface with parallel mean curvature vector field in a Riemannian product of two surfaces of constant Gaussian curvature carries a holomorphic quadratic differential. In this paper we consider the Riemannian product of a…
In this article, we study complete pseudo-Riemannian manifolds whose cone admits a parallel symmetric 2-tensorfield. The situation splits in three cases: nilpotent, decomposable or complex Riemannian. In the complex Riemannian and…
We examine the existence of tangent hyperplanes to subriemannian balls. Strictly abnormal shortest paths are allowed
Let $H \subset {\mathbb P}^n$ be a real-analytic subvariety of codimension one induced by a real-analytic curve in the Grassmannian $G(n+1,n)$. Assuming $H$ has a global defining function, we prove $H$ is Levi-flat, the closure of its…
We classify semi-Riemannian submersions with connected totally geodesic fibres from a real pseudo-hyperbolic space onto a semi-Riemannian manifold under the assumption that the dimension of the fibres is less than or equal to three and the…
We generalize techniques by Coskun, Riedl, and Yeong, and obtain an almost optimal bound on the degree for the algebraic hyperbolicity of very general hypersurfaces in rational homogeneous varieties. As examples, we work out the cases of…
There are several kinds of classification problems for real hypersurfaces in complex two-plane Grassmannians $G_2({\mathbb C}^{m+2})$. Among them, Suh classified Hopf hypersurfaces $M$ in $G_2({\mathbb C}^{m+2})$ with Reeb parallel Ricci…
It is pointed out that if we allow for the possibility of a multilayered universe, it is possible to maintain exact supersymmetry and arrange, in principle, for the vanishing of the cosmological constant. Superpartner(s) of a known particle…
We show that a complete, two-sided, stable minimal hypersurface in $\mathbf{R}^5$ is flat.
In this paper we prove some classification theorems of real hypersur- faces in Mn(c) satisfying certain conditions on the covariant derivative of the structure Jacobi operator. We also prove the non-existence of real hypersurfaces with…
Expansion of the two-component universe with arbitrary spatial curvature has been considered. It has been shown that the Friedmann integrals of the almost flat universe do not coincide.
A new $(1,1)$-dimensional super vector bundle which exists on any super Riemann surface is described. Cross-sections of this bundle provide a new class of fields on a super Riemann surface which closely resemble holomorphic functions on a…
In the present paper we study locally semiflat (we also call them semiintegrable) almost Grassmann structures. We establish necessary and sufficient conditions for an almost Grassmann structure to be alpha- or beta-semiintegrable. These…
In this paper, we have considered a new commuting condition, that is, $(R_\xi\phi) S = S (R_\xi\phi)$ \big(resp. $(\Bar{R}_N\phi) S = S (\Bar{R}_N\phi$)\big) between the restricted Jacobi operator~$R_\xi\phi$ (resp. $\Bar{R}_N\phi$), and…
We study grassmannians associated with a linear space with a nondegenerate hermitian form. The geometry of these grassmannians allows us to explain the relation between a (pseudo-)riemannian projective geometry and the conformal structure…
Let d_{k,n} and #_{k,n} denote the dimension and the degree of the Grassmannian G_{k,n} of k-planes in projective n-space, respectively. For each k between 1 and n-2 there are 2^{d_{k,n}} \cdot #_{k,n} (a priori complex) k-planes in P^n…
Let $X=G/K$ be a Riemannian symmetric space of the noncompact type and restricted root system $BC_2$ or $C_2$ (except $G=SO_0(p,2)$ with $p>2$ odd). The analysis of the meromorphic continuation of the resolvent of the Laplacian of $X$ is…
We study complete spacelike hypersurfaces immersed in an open region of the de Sitter space $\mathbb{S}^{n+1}_{1}$ which is known as the steady state space $\mathcal{H}^{n+1}$. In this setting, under suitable constraints on the behavior of…
We show that there is no phi-recurrent generalized Sasakian-space-forms, when is a non-zero constant.
The aim of the present paper is the study of real hypersurfaces equipped with the condition $\phi l = l \phi$, $l = R(., \xi, \xi)$.