相关论文: Real hypersurfaces equipped with pseudo-parallel s…

In this work we characterize certain immersed closed hypersurfaces of some ambient manifolds via the second eigenvalue of the Jacobi operator. First, we characterize the Clifford torus as the surface which maximizes the second eigenvalue of…

In this paper we study real hypersurfaces in the complex quadric space $Q^m$ whose structure Jacobi operator commutes with their structure tensor field. We show that the Reeb curvature $\alpha$ of such hypersurfaces is constant and if…

The non-existence of three dimensional real hypersurfaces in non-flat complex space forms with parallel *-Ricci tensor is proved.At the end of the papaer ideas for further research on *-Ricci tensor are provided.

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 classify all real hypersurfaces with constant principal curvatures in the complex hyperbolic plane.

Using the methods of moving frames and exterior differential systems, we show that there exist Hopf hypersurfaces in complex hyperbolic space CH^2 with any specified value of the Hopf principal curvature less than or equal to the…

Stark hypersurfaces are a special class of austere hypersurface in ${\mathbb C}P^n$ where the shape operator is compatible with the $CR$-structure. In this paper, the possible shape operators for stark hypersurfaces are completely…

In this paper, we study biconservative hypersurfaces of index 2 in $\mathbb E^{5}_{2}$. We give the complete classification of biconservative hypersurfaces with diagonalizable shape operator at exactly three distinct principal curvatures.…

We classify all real hypersurfaces with three distinct constant principal curvatures in complex hyperbolic spaces of dimension greater than two.

First, we classify proper biharmonic Hopf real hypersurfaces in $\mathbb{C}P^2$. Next, we classify proper biharmonic real hypersurfaces with two distinct principal curvatures in $\mathbb{C}P^n$, where $n\geq 2$. Finally, we prove that…

We classify isoparametric hypersurfaces in complex hyperbolic spaces.

It is proved the non-existence of Hopf hypersurfaces in $G_{2}({\Bbb C}^{m+2})$, $m \geq 3$, whose normal Jacobi operator is semi-parallel, if the principal curvature of the Reeb vector field is non-vanishing and the component of the Reeb…

In this paper, we give a construction of curvature-adapted hypersurfaces in the product $G_1/K_1\times G_2/K_2$ of (Riemannian) symmetric spaces $G_i/K_i$ ($i=1,2$). By this construction, we obtain many examples of curvature-adapted…

Using generalized Tanaka-Webster connection, we considered a real hypersurface $M$ in a complex two-plane Grassmannian $G_2({\mathbb C}^{m+2})$ when the GTW Reeb Lie derivative of the structure Jacobi operator coincides with the Reeb Lie…

We update and refine the work of T. Hamada concerning *-Einstein hypersurfaces in complex space forms CP^n and CH^n. We also address existence questions using the methods of moving frames and exterior differential systems.

We study various properties of quasimodular forms by using their connections with Jacobi-like forms and pseudodifferential operators. Such connections are made by identifying quasimodular forms for a discrete subgroup $\G$ of $SL(2, \bR)$…

There are three types of hypersurfaces in a pseudoconformal space C^n_1 of Lorentzian signature: spacelike, timelike, and lightlike. These three types of hypersurfaces are considered in parallel. Spacelike hypersurfaces are endowed with a…

We present the topological classification of real parts of real regular elliptic surfaces with a real section.

The almost contact metric structure that we have on a real hypersurface $M$ in the complex quadric $Q^{m}=SO_{m+2}/SO_mSO_2$ allows us to define, for any nonnull real number $k$, the $k$-th generalized Tanaka-Webster connection on $M$,…

It is known that hypersurfaces in $CP^n$ or $CH^n$ for which the number $g$ of distinct principal curvatures satisfied $g \le 2$ must belong to a standard list of Hopf hypersurfaces with constant principal curvatures, provided that $n \ge…