Laurian-Ioan Pişcoran

Wick–Tzitzeica solitons and their Monge–Ampér equation

We apply the Wick rotation to the Monge–Ampere equation of Tzitzeica graphs and we introduce the Wick–Tzitzeica solitons as complex functions solving the new equation. Some known Tzitzeica surfaces yields examples of these new solitons and we analyze them. To a second Wick–Tzitzeica soliton, we associate a homogeneous ODE system of gradient type which is Nambu–Poisson.

Projective flatness of a new class of ( α , β ) (\alpha,\beta) -metrics

Abstract In this paper we investigate a new ( α , β ) {(\alpha,\beta)} -metric F = β + a ⁢ α 2 + β 2 α {F=\beta+\frac{a\alpha^{2}+\beta^{2}}{\alpha}} , where α = a i ⁢ j ⁢ y i ⁢ y j {\alpha=\sqrt{{a_{ij}y^{i}y^{j}}}} is a Riemannian metric; β = b i ⁢ y i {\beta=b_{i}y^{i}} is a 1-form and a ∈ ( 1 4 , + ∞ ) {a\in(\frac{1}{4},+\infty)} is a real scalar. Also, we investigate the relationship between the geodesic coefficients of the metric F and the corresponding geodesic coefficients of the metric α.