Harmonic spheres in outer symmetric spaces, their canonical elements and Weierstrass-type representations

Stable Harmonic 2-spheres in Symmetric Spaces

TO = \ I l̂ l'vol. * J M A harmonic map 0 is said to be stable if the second variation of E at (j> is positive semidefinite. That is: for all smooth variations t)\t=0 > 0. Of particular interest is the case where M is the sphere S and N is a Riemannian symmetric space G/K. In this setting harmonic maps are branched minimal immersions, or the finite ...

Induced surfaces and their integrable dynamics. II. Generalized Weierstrass representations in 4D spaces and

Induced surfaces and their integrable dynamics. II. Generalized Weierstrass representations in 4D spaces and deformations via DS hierarchy. Abstract Extensions of the generalized Weierstrass representation to generic surfaces in 4D Euclidean and pseudo-Euclidean spaces are given. Geometric characteristics of surfaces are calculated. It is shown that integrable deformations of such induced surfa...

The Representations and Positive Type Functions of Some Homogenous Spaces

‎For a homogeneous spaces ‎$‎G/H‎$‎, we show that the convolution on $L^1(G/H)$ is the same as convolution on $L^1(K)$, where $G$ is semidirect product of a closed subgroup $H$ and a normal subgroup $K $ of ‎$‎G‎$‎. ‎Also we prove that there exists a one to one correspondence between nondegenerat $ast$-representations of $L^1(G/H)$ and representations of ...

A Fatou-type Theorem for Harmonic Functions on Symmetric Spaces

Minimal Immersions of Symmetric Spaces into Spheres