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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 vector field in the maximal quaternionic subbundle ${frak D}$ or its orthogonal complement ${frak D}^{bot}$ is invariant by the shape operator.
The aim of this paper is to prove a normal form Theorem for Dirac-Jacobi bundles using the recent techniques from Bursztyn, Lima and Meinrenken. As the most important consequence, we can prove the splitting theorems of Jacobi pairs which was proposed
We address the problem of determining the hypersurfaces $fcolon M^{n} to mathbb{Q}_s^{n+1}(c)$ with dimension $ngeq 3$ of a pseudo-Riemannian space form of dimension $n+1$, constant curvature $c$ and index $sin {0, 1}$ for which there exists another
We extend the construction of the BFV-complex of a coisotropic submanifold from the Poisson setting to the Jacobi setting. In particular, our construction applies in the contact and l.c.s. settings. The BFV-complex of a coisotropic submanifold $S$ co
In this paper, extending our previous joint work (Hu et al., Math Nachr 291:343--373, 2018), we initiate the study of Hopf hypersurfaces in the homogeneous NK (nearly Kahler) manifold $mathbf{S}^3timesmathbf{S}^3$. First, we show that any Hopf hypers
An isoparametric hypersurface in unit spheres has two focal submanifolds. Condition A plays a crucial role in the classification theory of isoparametric hypersurfaces in [CCJ07], [Chi16] and [Miy13]. This paper determines $C_A$, the set of points wit