On the geometrical properties of hypercomplex four-dimensional Lie groups

Autor:	Mansour Aghasi, Mehri Nasehi
Rok vydání:	2018
Předmět:	010101 applied mathematics Algebra Hypercomplex number Thesaurus (information retrieval) General Mathematics 010102 general mathematics Lie group Mathematics::Differential Geometry 0101 mathematics 01 natural sciences Mathematics
Zdroj:	Georgian Mathematical Journal. 27:111-120
ISSN:	1572-9176 1072-947X
DOI:	10.1515/gmj-2018-0003
Popis:	In this paper, we first classify Einstein-like metrics on hypercomplex four-dimensional Lie groups. Then we obtain the exact form of all harmonic maps on these spaces. We also calculate the energy of an arbitrary left-invariant vector field X on these spaces and determine all critical points for their energy functional restricted to vector fields of the same length. Furthermore, we give a complete and explicit description of all totally geodesic hypersurfaces of these spaces. The existence of Einstein hypercomplex four-dimensional Lie groups and the non-existence of non-trivial left-invariant Ricci and Yamabe solitons on these spaces are also proved.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::d33b03ba5edf5f760f11647f02f3f2c8 https://doi.org/10.1515/gmj-2018-0003 Zobrazit plný text záznamu