# The classification of biharmonic curves of Cartan-Vranceanu 3-dimensional spaces

@inproceedings{Caddeo2005TheCO, title={The classification of biharmonic curves of Cartan-Vranceanu 3-dimensional spaces}, author={Renzo Ilario Caddeo and Stefano Montaldo and C. Oniciuc and Paola Costantina Piu}, year={2005} }

In this article we characterize all biharmonic curves of the Cartan-Vranceanu 3-dimensional spaces and we give their explicit parametrizations.

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## 23 Citations

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## References

SHOWING 1-10 OF 19 REFERENCES

### Biharmonic submanifolds in spheres

- Mathematics
- 2002

We give some methods to construct examples of nonharmonic biharmonic submanifolds of the unitn-dimensional sphereSn. In the case of curves inSn we solve explicitly the biharmonic equation.

### BIHARMONIC SUBMANIFOLDS OF ${\mathbb S}^3$

- Mathematics
- 2001

We explicitly classify the nonharmonic biharmonic submanifolds of the unit three-dimensional sphere ${\mathbb S}^3$.

### Explicit Formulas for Non-Geodesic Biharmonic Curves of the Heisenberg Group

- Mathematics
- 2003

We consider the biharmonicity condition for maps between Riemann- ian manifolds (see (BK)), and study the non-geodesic biharmonic curves in the Heisenberg group H3. First we prove that all of them…

### Biharmonic curves in 3-dimensional Sasakian space forms

- Mathematics
- 2007

AbstractWe show that every proper biharmonic curve in a 3-dimensional Sasakian space form of constant holomorphic sectional curvature H is a helix (both of whose geodesic curvature and geodesic…

### On Additive Volume Invariants of Riemannian Manifolds

- Mathematics
- 2000

$(M, g)$ is flat, $B_{2k}\equiv 0$ for all $k\in N$ ; we have the following conjecture: VOLUME CONJECTURE [Gray and Vanhecke, 1979]. Assume that $V_{p}(r)=V_{0}(r)$ for any $p\in M$ and small…