Complete Riemannian Metrics with Holonomy Group~$G_2$ on Deformations of Cones over $S^3\times S^3$
Matematičeskie zametki, Tome 93 (2013) no. 5, pp. 645-657.

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

Complete Riemannian metrics with holonomy group $G_2$ on manifolds obtained by deformation of cones over $S^3 \times S^3$ are constructed.
Keywords: Riemannian metric, holonomy group $G_2$, metric on cones over $S^3 \times S^3$, vector bundle, Killing vector field.
@article{MZM_2013_93_5_a0,
     author = {Ya. V. Bazaikin and O. A. Bogojavlenskaja},
     title = {Complete {Riemannian} {Metrics} with {Holonomy} {Group~}$G_2$ on {Deformations} of {Cones} over $S^3\times S^3$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {645--657},
     publisher = {mathdoc},
     volume = {93},
     number = {5},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_5_a0/}
}
TY  - JOUR
AU  - Ya. V. Bazaikin
AU  - O. A. Bogojavlenskaja
TI  - Complete Riemannian Metrics with Holonomy Group~$G_2$ on Deformations of Cones over $S^3\times S^3$
JO  - Matematičeskie zametki
PY  - 2013
SP  - 645
EP  - 657
VL  - 93
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2013_93_5_a0/
LA  - ru
ID  - MZM_2013_93_5_a0
ER  - 
%0 Journal Article
%A Ya. V. Bazaikin
%A O. A. Bogojavlenskaja
%T Complete Riemannian Metrics with Holonomy Group~$G_2$ on Deformations of Cones over $S^3\times S^3$
%J Matematičeskie zametki
%D 2013
%P 645-657
%V 93
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2013_93_5_a0/
%G ru
%F MZM_2013_93_5_a0
Ya. V. Bazaikin; O. A. Bogojavlenskaja. Complete Riemannian Metrics with Holonomy Group~$G_2$ on Deformations of Cones over $S^3\times S^3$. Matematičeskie zametki, Tome 93 (2013) no. 5, pp. 645-657. http://geodesic.mathdoc.fr/item/MZM_2013_93_5_a0/

[1] Ya. V. Bazaikin, “O novykh primerakh polnykh nekompaktnykh metrik s gruppoi golonomii $\mathrm{Spin}(7)$”, Sib. matem. zhurn., 48:1 (2007), 11–32 | MR | Zbl

[2] Ya. V. Bazaikin, “Nekompaktnye rimanovy prostranstva s gruppoi golonomii $\operatorname{Spin}(7)$ i 3-sasakievy mnogoobraziya”, Geometriya, topologiya i matematicheskaya fizika. I, Sb. statei. K 70-letiyu so dnya rozhdeniya akademika Sergeya Petrovicha Novikova, Tr. MIAN, 263, MAIK, M., 2008, 6–17 | MR | Zbl

[3] Ya. V. Bazaikin, E. G. Malkovich, “$\mathrm{Spin}(7)$-struktury na kompleksnykh lineinykh rassloeniyakh i yavnye rimanovy metriki s gruppoi golonomii $\mathrm{SU}(4)$”, Matem. sb., 202:4 (2011), 3–30 | DOI | MR

[4] E. G. Malkovich, “O novykh yavnykh rimanovykh metrikakh s gruppoi golonomii $SU(2(n+1))$”, Sib. matem. zhurn., 52:1 (2011), 95–99 | MR | Zbl

[5] A. Brandhuber, J. Gomis, S. S. Gubser, S. Gukov, “Gauge theory at large $N$ and new $G_2$ holonomy metrics”, Nuclear Phys. B, 611:1-3 (2001), 179–204, arXiv: hep-th/0106034v2 | DOI | MR | Zbl

[6] M. Cvetič, G. W. Gibbons, H. Lü, C. N. Pope, “Cohomogeneity one manifolds of $\mathrm{Spin}(7)$ and $G_2$ holonomy”, Phys. Rev. D (3), 65:10 (2002), 106004, arXiv: hep-th/0108245v2 | DOI | MR

[7] M. Cvetič, G. W. Gibbons, H. Lü, C. N. Pope, “Orientifolds and slumps in $G_2$ and $\mathrm{Spin}(7)$ metrics”, Ann. Phys., 310:2 (2004), 265–301, arXiv: hep-th/0111096v2 | DOI | MR | Zbl

[8] A. Brandhuber, “$G_2$ holonomy spaces from invariant three-forms”, Nuclear Phys. B, 629:1-3 (2002), 393–416, arXiv: hep-th/0112113v2 | DOI | MR | Zbl

[9] M. Cvetič, G. W. Gibbons, H. Lü, C. N. Pope, “A $G_2$ unification of the deformed and resolved conifolds”, Phys. Lett. B, 534:1-4 (2002), 172–180, arXiv: hep-th/0112138v3 | DOI | MR | Zbl

[10] Z. W. Chong, M. Cvetič, G. W. Gibbons, H. Lü, C. N. Pope, P. Wagner, “General metrics of $G_2$ holonomy and contraction limits”, Nuclear Phys. B, 638:3 (2002), 459–482, arXiv: hep-th/0204064v1 | DOI | MR | Zbl

[11] R. L. Bryant, S. M. Salamon, “On the construction of some complete metrics with exceptional holonomy”, Duke Math. J., 58:3 (1989), 829–850 | DOI | MR | Zbl

[12] G. W. Gibbons, D. N. Page, C. N. Pope, “Einstein Metrics on $S^3$, $\mathbb{R}^3$, and $\mathbb{R}^4$ bundles”, Comm. Math. Phys., 127:3 (1990), 529–553 | DOI | MR | Zbl