Etemad Dehkordy A.
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.
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.