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ЖУРНАЛЫ // Журнал математической физики, анализа, геометрии // Архив

Журн. матем. физ., анал., геом., 2007, том 3, номер 2, страницы 253–276 (Mi jmag62)

Invariant totally geodesic unit vector fields on three-dimensional Lie groups

A. Yampolsky

Department of Mechanics and Mathematics, V.N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv, 61077, Ukraine

Аннотация: We give a complete list of left-invariant unit vector fields on three-dimensional Lie groups equipped with a left-invariant metric that generate a totally geodesic submanifold in the unit tangent bundle of a group equipped with the Sasaki metric. As a result we obtain that each three-dimensional Lie group admits totally geodesic unit vector field under some conditions on structural constants. From a geometrical viewpoint, the field is either parallel or a characteristic vector field of a natural almost contact structure on the group.

Ключевые слова и фразы: Sasaki metric, totally geodesic unit vector field, almost contact structure, Sasakian structure.

MSC: Primary 53B20, 53B25; Secondary 53C25

Поступила в редакцию: 22.03.2006

Язык публикации: английский



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