Macias-Virgós, Enrique; Sanmartín-Carbón, Esperanza Minimal foliations on Lie groups. (English) Zbl 0766.53021 Indag. Math., New Ser. 3, No. 1, 41-46 (1992). Let \(G\) be a connected Lie group, \(H\) a connected, not necessarily closed, Lie subgroup of \(G\). The authors discuss minimality of foliations \(F(G,H)\). In R. Takagi and S. Yorozu [Tohoku Math. J., II. Ser. 36, 541-554 (1984; Zbl 0559.53018)] it is proved that if a left invariant Riemannian metric \(g\) is \(\text{Ad}(H)\)-invariant then \(g\) is bundle-like for \(F(G,H)\) and \(F(G,H)\) is totally geodesic for \(g\). In this paper, the authors prove that there always exists a (bundle-like) Riemannian metric on \(G\) for which the leaves of \(F(G,H)\) are minimal submanifolds. Reviewer: Hou Zixin (Tianjin) Cited in 2 Documents MSC: 53C12 Foliations (differential geometric aspects) 57R30 Foliations in differential topology; geometric theory 22E15 General properties and structure of real Lie groups Keywords:minimal submanifolds Citations:Zbl 0559.53018 PDFBibTeX XMLCite \textit{E. Macias-Virgós} and \textit{E. Sanmartín-Carbón}, Indag. Math., New Ser. 3, No. 1, 41--46 (1992; Zbl 0766.53021) Full Text: DOI References: [1] Fédida, E., Feuilletages de Lie (1983), Thèse Strasbourg · Zbl 0218.57014 [2] Ghys, E., Feuilletages riemanniens sur les variétés simplement connexes, Ann. Inst. Fourier, Grenoble, 34, 4, 203-223 (1984) · Zbl 0525.57024 [3] Haefliger, A., Some remarks on foliations with minimal leaves, Journal of Diff. Geom., 15, 269-284 (1980) · Zbl 0444.57016 [4] Maľcev, A., On the simple connectedness of invariant subgroups of the Lie groups, Acad. Sci. U.R.S.S., 34, 10-13 (1942) · Zbl 0061.04605 [5] Molino, P., Riemannian Foliations, Progress in Math., Vol. 73 (1988), Birkaüser [6] Takagi, R.; Yorozu, S., Minimal foliations on Lie groups, Tohoku Math. J., 36, 541-554 (1984) · Zbl 0559.53018 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.