Petrov I. Geometry of submanifolds in nilpotent Lie groups and Lie groups with biinvariant metric

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0408U004720

Thesis Registration Form

0408U004720.pdf

Applicant for

Specialization

  • 01.01.04 - Геометрія і топологія

10-10-2008

Specialized Academic Board

К64.051.11

Essay

The harmonicity criteria for the Gauss map of a submanifold in Lie group for the general case and for some special cases are obtained. It is shown that the parallelism of the mean curvature field is not equivalent to the harmonicity of the Gauss map for submanifolds in Lie groups with biinvariant metric and in the Heisenberg groups. It is shown that a constant mean curvature surface with the harmonic Gauss map in the three-dimensional Heisenberg group is a "cylinder".

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