相关论文: On the geometry of biharmonic submanifolds in Sasa…
We classify the biharmonic Legendre curves in a Sasakian space form, and obtain their explicit parametric equations in the $(2n+1)$-dimensional unit sphere endowed with the canonical and deformed Sasakian structures defined by Tanno. Then,…
We consider biharmonic submanifolds in both generalized complex and Sasakian space forms. After giving the biharmonicity conditions for submanifolds in these spaces, we study different particular cases for which we obtain curvature…
We obtain the parametric equations of all biharmonic Legendre curves and Hopf cylinders in the 3-dimensional unit sphere endowed with the modified Sasakian structure defined by Tanno.
We find the characterization of maximum dimensional proper-biharmonic integral $\mathcal{C}$-parallel submanifolds of a Sasakian space form and then classify such submanifolds in a 7-dimensional Sasakian space form. Working in the sphere…
We study the Boothby-Wang fibration of para-Sasakian manifolds and introduce the class of para-Sasakian $\phi$-symmetric spaces, canonically fibering over para-Hermitian symmetric spaces. Using this fibration we give a method to explicitly…
In this paper we give necessary and sufficient conditions for spacelike and timelike curves in a conformally flat, quasi conformally flat and conformally symmetric 4-dimensional \textit{LP}-Sasakian manifold to be proper biharmonic. Also,…
Sasakian manifolds provide explicit formulae of some Jacobi operators which describe the biharmonic equation of curves in Riemannian manifolds. In this paper we characterize non-geodesic biharmonic curves in Sasakian manifolds which are…
In [5], D. Fetcu and C. Oniciuc presented the classification result for biharmonic $\mathcal{C}$-parallel Legendrian submanifolds in $7$-dimensional Sasakian space forms. However, it is incomplete. In this paper, all such submanifolds are…
We consider interpolating sesqui-harmonic Legendre curves in Sasakian space forms. We find the necessary and sufficient conditions for Legendre curves in Sasakian space forms to be interpolating sesqui-harmonic. Finally, we obtain an…
We give some general results on proper-biharmonic submanifolds of a complex space form and, in particular, of the complex projective space. These results are mainly concerned with submanifolds with constant mean curvature or parallel mean…
We provide a construction method for biharmonic submanifolds in cohomogeneity one manifolds. In particular, we give new examples of biharmonic submanifolds and study the normal index of these submanifolds. We use this strategy to construct…
We classify the biharmonic non-Legendre curves in a Sasakian space form for which the angle between the tangent vector field and the characteristic vector field is constant and obtain explicit examples of such curves in…
In this article we consider the concept of biharmonicity about the hypersurfaces in the Sasakian space form which is equipped with the Tanaka-Webster connection.
We investigate proper biharmonic hypersurfaces with at most three distinct principal curvatures in space forms. We obtain the full classification of proper biharmonic hypersurfaces in 4-dimensional space forms.
We study f-biharmonic and bi-f-harmonic submanifolds in both generalized complex and Sasakian space forms. We prove necessary and sufficient condition for f-biharmonicity and bi-f-harmonicity in the general case and many particular cases.…
We classify biharmonic submanifolds with certain geometric properties in Euclidean spheres. For codimension 1, we determine the biharmonic hypersurfaces with at most two distinct principal curvatures and the conformally flat biharmonic…
A hypersurface is said to be totally biharmonic if all its geodesics are biharmonic curves in the ambient space. We prove that a totally biharmonic hypersurface into a space form is an isoparametric biharmonic hypersurface, which allows us…
We classify the space-like biharmonic surfaces in 3-dimension pseudo-Riemannian space form, and construct explicit examples of proper biharmonic hypersurfaces in general ADS space.
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 characterize biharmonic anti-invariant surfaces in $3$-dimensional generalized $(\kappa, \mu)$-manifolds with non-zero constant mean curvature by means of the scalar curvature of the ambient space and the mean curvature. In addition, we…