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D. Fetcu

Publications and source records attributed to D. Fetcu.

5 recordsLinked to original sources
arXiv2010

Biharmonic integral $\mathcal{C}$-parallel submanifolds in 7-dimensional Sasakian space forms

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 $\mathbb{S}^7$ we explicitly find all 3-dimensional proper-biharmonic integral $C$-parallel submanifolds. We also determine the proper-biharmonic parallel Lagrangian submanifolds of $\mathbb{C}P^3$.

math.DG↗
arXiv2009

Biharmonic submanifolds of $\mathbb{C}P^n$

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 curvature vector field. We find the relation between the bitension field of the inclusion of a submanifold $\bar{M}$ in $\mathbb{C}P^n$ and the bitension field of the inclusion of the corresponding Hopf-tube in $\mathbb{S}^{2n+1}$. Using this relation we produce new families of proper-biharmonic submanifolds of $\mathbb{C}P^n$. We study the geometry of biharmonic curves of $\mathbb{C}P^n$ and we characterize the proper-biharmonic curves in terms of their curvatures and complex torsions.

math.DG↗
arXiv2008

On the geometry of biharmonic submanifolds in Sasakian space forms

We classify all proper-biharmonic Legendre curves in a Sasakian space form and point out some of their geometric properties. Then we provide a method for constructing anti-invariant proper-biharmonic submanifolds in Sasakian space forms. Finally, using the Boothby-Wang fibration, we determine all proper-biharmonic Hopf cylinders over homogeneous real hypersurfaces in complex projective spaces.

math.DG↗
arXiv2007

Explicit formulas for biharmonic submanifolds in Sasakian space forms

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, composing with the flow of the Reeb vector field, we transform a biharmonic integral submanifold into a biharmonic anti-invariant submanifold. Using this method we obtain new examples of biharmonic submanifolds in spheres and, in particular, in $\mathbb{S}^{7}$.

math.DG↗