Minimal Lagrangian isotropic immersions in indefinite complex space forms

Let Mⁿ be an n-dimensional (n≥3) minimal Lagrangian isotropic submanifold in an indefinite complex space form. We show that the dimension of Mⁿ satisfies n=3r+2 with r, a positive integer. When n<14, we give a classification of such submanifolds.     

Lagrangian surfaces in the complex hyperquadric Q2

In this paper, we introduce a one-form $\Phi$ associated to a Lagrangian immersion $f$ from Riemann surface $M$ into the complex hyperquadric $Q_2$. It is proved that $f$ is minimal if and only if $\Phi$ is vanishing and $f$ is H-minimal if and only if $\Phi$ is holomorphic. As an application, a family of $S^1$-equivariant minimal Lagrangian tori in $Q_2$ are obtained.     

Symmetry in extended phase space for singular Lagrangian with subsidiary constraints

A generalization of the Noether theorem to a singular nonholonomic system in the canonical formalism is given and its inverse theorem is presented. Based on the canonical action integral, a generalization of the Poincaré-Cartan integral invariant of a singular nonholonomic system is obtained. It is shown that this invariant is equivalent to the canonical equations of a singular constrained system. Some confusions in the literature are corrected. An example is given.     

The forms of three-order Lagrangian equation in relative motion

In this paper, the general expressions of three-order Lagrangian equations in a motional coordinate system are obtained. In coordinate systems with some specific forms of motion, the expressions corresponding to these equations are also presented.     

A perceptual space for underwater man-made sounds towards target classification

This work is the second part in a series of studies about the auditory features for underwater target classification, focusing on man-made vehicle targets (i.e. submarines, patrol boats and large surface ships). A psychoacoustic method, which is suitable for a small number of samples, was used. An optimal model with three common dimensions, specificities and latent classes was selected on the basis of the dissimilarity ratings among representative sounds and with the use of an extended version of the multidimensional scaling algorithm CLASCAL. However, such a three-dimensional space could not absolutely separate targets, whereas the first dimension in the four-dimensional space discriminated the submarines, patrol boats and ships; thus, the four-dimensional space was superior in target classification. The stepwise regression method was used to establish the relationships between individual dimensions and typical auditory features. Results showed that the first dimension was represented by the linear combination of zero-crossing rate and spectral variation, whereas the second dimension was described by attack slope. The last two dimensions were not associated with any features, and they were proved to include meaningless data noises. Finally, through a contrastive analysis, the perceptual space obtained in this study was found to be a good ‘local’ representation of the space in the first part of the study series.     

A complex minkowski space approach to twistors

This paper is basically a review of known results in twistor theory. Its value is intended to lie in the connections presented between twistor concepts and structures in complex Minkowski space. The relationship of twistor theory to complex null infinity and a new proof of the Kerr theorem are presented; these results are to some extent original.     

Semi-symmetric Lorentzian hypersurfaces in Lorentzian space forms

In the present paper, we shall investigate and classify Lorentzian hypersurfaces in Lorentzian space forms satisfying some curvature conditions. We shall focus especially on semi-symmetric Lorentzian hypersurfaces. Those of constant curvature and those so-called “good” are explicitly described and classified. We shall also classify Einstein–Lorentzian hypersurfaces.     

On time-like Willmore surfaces in Minkowski space

We study time-like surfaces in Minkowski space, which are critical points of the Willmore energy. Transforming the fourth order Willmore equation into a quasi-linear, second order hyperbolic system, we prove existence, uniqueness and symmetry properties of such surfaces, subject to geometric initial conditions.     

On the Lagrangian theory of anti-self-dual fields in four-dimensional euclidean space

We show that a certain four-dimensional field theory has powerful structures in common with the two-dimensional 0(1, 3) non-linear -model.     

Ribaucour transformations for isometric immersions of pseudo-Riemannian space forms

In this paper, we give the explicit construction for isometric immersions of pseudo-Riemannian space forms via loop group actions. As a consequence, we obtain a Ribaucour transformation and its permutability theorem for isometric immersions of pseudo-Riemannian space forms, which is a generalization of the permutability theorem for surfaces in R³$R^3$, and a family of new isometric immersions of the pseudo-Riemannian space forms from a given one via a purely algebraic algorithm.