$\mathrm{Spin}(7)$-structures on complex linear bundles and explicit Riemannian metrics with holonomy group
Sbornik. Mathematics, Tome 202 (2011) no. 4, pp. 467-493

Voir la notice de l'article provenant de la source Math-Net.Ru

A system of differential equations with 5 unknowns is fully investigated; this system is equivalent to the existence of a parallel $\mathrm{Spin}(7)$-structure on a cone over a 3-Sasakian manifold. A continuous one-parameter family of solutions to this system is explicitly constructed; it corresponds to metrics with a special holonomy group, $\mathrm{SU}(4)$, which generalize Calabi's metrics. Bibliography: 10 titles.
Keywords: holonomy group, 3-Sasakian manifold.
@article{SM_2011_202_4_a0,
     author = {Ya. V. Bazaikin and E. G. Malkovich},
     title = {$\mathrm{Spin}(7)$-structures on complex linear bundles and explicit {Riemannian} metrics with holonomy group},
     journal = {Sbornik. Mathematics},
     pages = {467--493},
     publisher = {mathdoc},
     volume = {202},
     number = {4},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2011_202_4_a0/}
}
TY  - JOUR
AU  - Ya. V. Bazaikin
AU  - E. G. Malkovich
TI  - $\mathrm{Spin}(7)$-structures on complex linear bundles and explicit Riemannian metrics with holonomy group
JO  - Sbornik. Mathematics
PY  - 2011
SP  - 467
EP  - 493
VL  - 202
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2011_202_4_a0/
LA  - en
ID  - SM_2011_202_4_a0
ER  - 
%0 Journal Article
%A Ya. V. Bazaikin
%A E. G. Malkovich
%T $\mathrm{Spin}(7)$-structures on complex linear bundles and explicit Riemannian metrics with holonomy group
%J Sbornik. Mathematics
%D 2011
%P 467-493
%V 202
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2011_202_4_a0/
%G en
%F SM_2011_202_4_a0
Ya. V. Bazaikin; E. G. Malkovich. $\mathrm{Spin}(7)$-structures on complex linear bundles and explicit Riemannian metrics with holonomy group. Sbornik. Mathematics, Tome 202 (2011) no. 4, pp. 467-493. http://geodesic.mathdoc.fr/item/SM_2011_202_4_a0/