2019
Том 71
№ 7

### All Issues

Articles: 2
Article (English)

### A study on tensor product surfaces in low-dimensional Euclidean spaces

Ukr. Mat. Zh. - 2012. - 64, № 12. - pp. 1630-1640

We consider a special case for curves in two-, three-, and four-dimensional Euclidean spaces and obtain a necessary and sufficient condition for the tensor product surfaces of the planar unit circle centered at the origin and these curves to have a harmonic Gauss map.

Brief Communications (English)

### First eigenvalue of the Laplace operator and mean curvature

Ukr. Mat. Zh. - 2008. - 60, № 7. - pp. 1000–1003

The main theorem of this paper states a relation between the first nonzero eigenvalue of the Laplace operator and the squared norm of mean curvature in irreducible compact homogeneous manifolds under spatial conditions. This statement has some consequences presented in the remainder of paper.