Geodesic
Almost Kähler structures on complex hyperbolic space
Filomat, Tome 37 (2023) no. 25, p. 8661

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DOI

Complex hyperbolic space has the structure of a solvable Lie group. Based on the recent classification of Riemannian left-invariant metrics we describe all left-invariant almost Kähler structures on that group. The only Kähler structure is the standard structure of the complex hyperbolic space and all others are strictly almost Kähler. We calculated the Chern connection and obtained the characterization by its torsion tensor. It is proved that the only SCF-soliton is the Kähler one.
DOI : 10.2298/FIL2325661D
Classification : 53C15, 53B355, 53D30
Keywords: Complex hyperbolic space, Almost Kähler structures 
Andrijana Dekić. Almost Kähler structures on complex hyperbolic space. Filomat, Tome 37 (2023) no. 25, p. 8661 . doi: 10.2298/FIL2325661D
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     author = {Andrijana Deki\'c},
     title = {Almost {K\"ahler} structures on complex hyperbolic space},
     journal = {Filomat},
     pages = {8661 },
     year = {2023},
     volume = {37},
     number = {25},
     doi = {10.2298/FIL2325661D},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2325661D/}
}
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