caa a22 4500 605496412 CHVBK 20210128100536.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10231-014-0412-8 doi (NATIONALLICENCE)springer-10.1007/s10231-014-0412-8 Minimality of invariant submanifolds in metric contact pair geometry [Elektronische Daten] [Gianluca Bande, Amine Hadjar] We study invariant submanifolds of manifolds endowed with a normal or complex metric contact pair with decomposable structure tensor $$\phi $$ ϕ . For the normal case, we prove that a $$\phi $$ ϕ -invariant submanifold tangent to a Reeb vector field and orthogonal to the other one is minimal. For a $$\phi $$ ϕ -invariant submanifold $$N$$ N everywhere transverse to both the Reeb vector fields but not orthogonal to them, we prove that it is minimal if and only if the angle between the tangential component $$\xi $$ ξ (with respect to $$N$$ N ) of a Reeb vector field and the Reeb vector field itself is constant along the integral curves of $$\xi $$ ξ . For the complex case (when just one of the two natural almost complex structures is supposed to be integrable), we prove that a complex submanifold is minimal if and only if it is tangent to both the Reeb vector fields. Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 Contact pair nationallicence Vaisman manifold nationallicence Invariant submanifold nationallicence Minimal submanifold nationallicence Bande Gianluca Dipartimento di Matematica e Informatica, Università degli Studi di Cagliari, Via Ospedale 72, 09124, Cagliari, Italy aut Hadjar Amine Laboratoire de Mathématiques, Informatique et Applications, Université de Haute Alsace, 4 Rue des Frères Lumière, 68093, Mulhouse, France aut Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/4(2015-08-01), 1107-1122 0373-3114 194:4<1107 2015 194 10231 https://doi.org/10.1007/s10231-014-0412-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10231-014-0412-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bande Gianluca Dipartimento di Matematica e Informatica, Università degli Studi di Cagliari, Via Ospedale 72, 09124, Cagliari, Italy aut NATIONALLICENCE 700 1- Hadjar Amine Laboratoire de Mathématiques, Informatique et Applications, Université de Haute Alsace, 4 Rue des Frères Lumière, 68093, Mulhouse, France aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/4(2015-08-01), 1107-1122 0373-3114 194:4<1107 2015 194 10231