In this work, the notion of a slant helix is extended to the space E. First, we introduce the type-2 harmonic curvatures of a regular curve. Thereafter, by using this, we present some necessary and sufficient conditions for a curve to be a slant helix in Euclidean n-space. We also express some integral characterizations of such curves in terms of the curvature functions. Finally, we give some c...

We consider random conformally invariant paths in the complex plane (SLEs). Using the Coulomb gas method in conformal field theory, we rederive the mixed multifractal exponents associated with both the harmonic measure and winding (rotation or monodromy) near such critical curves, previously obtained by quantum gravity methods. The results also extend to the general cases of harmonic measure mo...

Dedicated to Professor WeiYue Ding on the occasion of his 60th birthday Abstract For k ≥ 3, we establish new estimate on Hausdorff dimensions of the singular set of stable-stationary harmonic maps to the sphere S. We show that the singular set of stable-stationary harmonic maps from B to S is the union of finitely many isolated singular points and finitely many Hölder continuous curves. We also...

In this paper, we determine necessary and sufficient conditions for a non-Frenet Legendre curve to be $f$-harmonic, $f$-biharmonic, bi-$f$-harmonic, biminimal $f$-biminimal in three-dimensional normal almost paracontact metric manifold. Besides, obtain some nonexistence theorems.

The large N spectrum of the quantum mechanical hamiltonian of two hermitean matrices in a harmonic potential is studied in a framework where one of the matrices is treated exactly and the other is treated as a creation operator impurity in the background of the first matrix. For the free case, the complete set of invariant eigenstates and corresponding energies are obtained. When g YM interacti...

In order to investigate the dynamic properties of the flux line lattice, the temperature dependencies of the basic and Ž . higher harmonic complex AC susceptibilities have been analysed. In particular, the first i.e., fundamental and the third Ž . X Ž . Y Ž . harmonic x T sx T q ix T , have been measured at different frequencies, and the measurements have been 1,3 1,3 1,3 compared with both ana...

Fractal geometry of random curves appearing in the scaling limit of critical two-dimensional statistical systems is characterized by their harmonic measure and winding angle. The former is the measure of the jaggedness of the curves while the latter quantifies their tendency to form logarithmic spirals. We show how these characteristics are related to local operators of conformal field theory a...