Minimality of invariant submanifolds in metric contact pair geometry
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| 024 | 7 | 0 | |a 10.1007/s10231-014-0412-8 |2 doi |
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| 245 | 0 | 0 | |a Minimality of invariant submanifolds in metric contact pair geometry |h [Elektronische Daten] |c [Gianluca Bande, Amine Hadjar] |
| 520 | 3 | |a 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. | |
| 540 | |a Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 | ||
| 690 | 7 | |a Contact pair |2 nationallicence | |
| 690 | 7 | |a Vaisman manifold |2 nationallicence | |
| 690 | 7 | |a Invariant submanifold |2 nationallicence | |
| 690 | 7 | |a Minimal submanifold |2 nationallicence | |
| 700 | 1 | |a Bande |D Gianluca |u Dipartimento di Matematica e Informatica, Università degli Studi di Cagliari, Via Ospedale 72, 09124, Cagliari, Italy |4 aut | |
| 700 | 1 | |a Hadjar |D Amine |u Laboratoire de Mathématiques, Informatique et Applications, Université de Haute Alsace, 4 Rue des Frères Lumière, 68093, Mulhouse, France |4 aut | |
| 773 | 0 | |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/4(2015-08-01), 1107-1122 |x 0373-3114 |q 194:4<1107 |1 2015 |2 194 |o 10231 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-014-0412-8 |q text/html |z Onlinezugriff via DOI |
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| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
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| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10231-014-0412-8 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Bande |D Gianluca |u Dipartimento di Matematica e Informatica, Università degli Studi di Cagliari, Via Ospedale 72, 09124, Cagliari, Italy |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Hadjar |D Amine |u Laboratoire de Mathématiques, Informatique et Applications, Université de Haute Alsace, 4 Rue des Frères Lumière, 68093, Mulhouse, France |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/4(2015-08-01), 1107-1122 |x 0373-3114 |q 194:4<1107 |1 2015 |2 194 |o 10231 | ||