Invariant Totally Geodesic Unit Vector Fields on Three-Dimensional Lie Groups

Автор(и)

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

Анотація

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.

Mathematics Subject Classification: 53B20, 53B25, 53C25.

Ключові слова:

Sasaki metric, totally geodesic unit vector field, almost contact structure, Sasakian structure.

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Як цитувати

(1)
Yampolsky, A. Invariant Totally Geodesic Unit Vector Fields on Three-Dimensional Lie Groups. Журн. мат. фіз. анал. геом. 2007, 3, 253-276.

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