Some classes of almost Hermitian structures that can be realized on $S^6$
Sbornik. Mathematics, Tome 214 (2023) no. 5, pp. 732-743 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Structures of cohomogeneity one on $S^6$ are under investigation. Examples of semi-Kähler and quasi-Kähler structures are constructed. Questions concerning the existence of almost Hermitian structures of cohomogeneity one on a round sphere are investigated. Bibliography: 14 titles.
Keywords: almost Hermitian structures, $6$-sphere, structures of cohomogeneity one.
@article{SM_2023_214_5_a4,
     author = {N. A. Daurtseva},
     title = {Some classes of almost {Hermitian} structures that can be realized on~$S^6$},
     journal = {Sbornik. Mathematics},
     pages = {732--743},
     year = {2023},
     volume = {214},
     number = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2023_214_5_a4/}
}
TY  - JOUR
AU  - N. A. Daurtseva
TI  - Some classes of almost Hermitian structures that can be realized on $S^6$
JO  - Sbornik. Mathematics
PY  - 2023
SP  - 732
EP  - 743
VL  - 214
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/SM_2023_214_5_a4/
LA  - en
ID  - SM_2023_214_5_a4
ER  - 
%0 Journal Article
%A N. A. Daurtseva
%T Some classes of almost Hermitian structures that can be realized on $S^6$
%J Sbornik. Mathematics
%D 2023
%P 732-743
%V 214
%N 5
%U http://geodesic.mathdoc.fr/item/SM_2023_214_5_a4/
%G en
%F SM_2023_214_5_a4
N. A. Daurtseva. Some classes of almost Hermitian structures that can be realized on $S^6$. Sbornik. Mathematics, Tome 214 (2023) no. 5, pp. 732-743. http://geodesic.mathdoc.fr/item/SM_2023_214_5_a4/

[1] E. Calaby and H. Gluck, “What are the best almost-complex structures on the 6-sphere?”, Differential geometry: geometry in mathematical physics and related topics, Part 2 (Los Angeles, CA 1990), Proc. Sympos. Pure Math., 54, Part 2, Amer. Math. Soc., Providence, RI, 1993, 99–106 | DOI | MR | Zbl

[2] T. Friedrich, “Nearly Kähler and nearly parallel $G_2$-structures on spheres”, Arch. Math. (Brno), 42:5 (2006), 241–243 | MR | Zbl

[3] C. LeBrun, “Orthogonal complex structures on $S^6$”, Proc. Amer. Math. Soc., 101:1 (1987), 136–138 | DOI | MR | Zbl

[4] G. Bor and L. Hernández-Lamoneda, “The canonical bundle of a Hermitian manifold”, Bol. Soc. Mat. Mexicana (3), 5:1 (1999), 187–198 | MR | Zbl

[5] L. Foscolo and M. Haskins, “New $G_2$-holonomy cones and exotic nearly Kähler structures on $S^6$ and $S^3\times S^3$”, Ann. of Math. (2), 185:1 (2017), 59–130 | DOI | MR | Zbl

[6] A. Gray and L. M. Hervella, “The sixteen classes of almost Hermitian manifolds and their linear invariants”, Ann. Mat. Pura Appl. (4), 123 (1980), 35–58 | DOI | MR | Zbl

[7] P. S. Mostert, “On a compact Lie group acting on a manifold”, Ann. of Math. (2), 65:3 (1957), 447–455 | DOI | MR | Zbl

[8] L. Bérard-Bergery, “Sur de nouvelles variétés riemanniennes d'Einstein”, Inst. Élie Cartan, 6, Univ. Nancy, Nancy, 1982, 1–60 | MR | Zbl

[9] G. E. Bredon, Introduction to compact transformation groups, Pure Appl. Math., 46, Academic Press, New York–London, 1972, xiii+459 pp. | MR | Zbl

[10] F. Podestà and A. Spiro, “Six-dimensional nearly Kähler manifolds of cohomogeneity one”, J. Geom. Phys., 60:2 (2010), 156–164 | DOI | MR | Zbl

[11] F. Podestà and A. Spiro, “Six-dimensional nearly Kähler manifolds of cohomogeneity one (II)”, Comm. Math. Phys., 312:2 (2012), 477–500 | DOI | MR | Zbl

[12] P. Candelas and X. C. de la Ossa, “Comments on conifolds”, Nuclear Phys. B, 342:1 (1990), 246–268 | DOI | MR

[13] N. Hitchin, “Stable forms and special metrics”, Global differential geometry: the mathematical legacy of Alfred Gray (Bilbao 2000), Contemp. Math., 288, Amer. Math. Soc., Providence, RI, 2001, 70–89 | DOI | MR | Zbl

[14] N. A. Daurtseva, “Quasi-Kähler structures of cohomogeneity 1 on $S^2\times S^4$”, Siberian Math. J., 61:4 (2020), 600–609 | DOI | MR | Zbl