Scalar Curvatures of Invariant Almost Hermitian Structures on Generalized Flag Manifolds
Symmetry, integrability and geometry: methods and applications, Tome 17 (2021)

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In this paper we study invariant almost Hermitian geometry on generalized flag manifolds. We will focus on providing examples of Kähler like scalar curvature metric, that is, almost Hermitian structures $(g,J)$ satisfying $s=2s_{\rm C}$, where $s$ is Riemannian scalar curvature and $s_{\rm C}$ is the Chern scalar curvature.
Keywords: curvature of almost Hermitian structures, generalized flag manifolds, Kähler like scalar curvature.
Lino Grama; Ailton R. Oliveira. Scalar Curvatures of Invariant Almost Hermitian Structures on Generalized Flag Manifolds. Symmetry, integrability and geometry: methods and applications, Tome 17 (2021). http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a108/
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     title = {Scalar {Curvatures} of {Invariant} {Almost} {Hermitian} {Structures} on {Generalized} {Flag} {Manifolds}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2021},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a108/}
}
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[1] Alekseevsky D. V., “Flag manifolds”, Zb. Rad. Mat. Inst. Beograd. (N.S.), 6 (1997), 3–35 | MR | Zbl

[2] Apostolov V., Drăghici T., “Almost Kähler 4-manifolds with $J$-invariant Ricci tensor and special Weyl tensor”, Q. J. Math., 51 (2000), 275–294, arXiv: math.DG/9911196 | DOI | MR | Zbl

[3] Arvanitoyeorgos A., “Geometry of flag manifolds”, Int. J. Geom. Methods Mod. Phys., 3 (2006), 957–974 | DOI | MR | Zbl

[4] Arvanitoyeorgos A., Chrysikos I., “Invariant Einstein metrics on generalized flag manifolds with two isotropy summands”, J. Aust. Math. Soc., 90 (2011), 237–251, arXiv: 0902.1826 | DOI | MR | Zbl

[5] Arvanitoyeorgos A., Chrysikos I., Sakane Y., “Homogeneous Einstein metrics on $G_2/T$”, Proc. Amer. Math. Soc., 141 (2013), 2485–2499, arXiv: 1010.3661 | DOI | MR | Zbl

[6] Besse A. L., Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 10, Springer-Verlag, Berlin, 1987 | DOI | MR | Zbl

[7] Borel A., Hirzebruch F., “Characteristic classes and homogeneous spaces. I”, Amer. J. Math., 80 (1958), 458–538 | DOI | MR

[8] Chern S.-S., “Characteristic classes of Hermitian manifolds”, Ann. of Math., 47 (1946), 85–121 | DOI | MR | Zbl

[9] Dabkowski M. G., Lock M. T., “An equivalence of scalar curvatures on Hermitian manifolds”, J. Geom. Anal., 27 (2017), 239–270, arXiv: 1505.02726 | DOI | MR | Zbl

[10] Friedrich T., Ivanov S., “Parallel spinors and connections with skew-symmetric torsion in string theory”, Asian J. Math., 6 (2002), 303–335, arXiv: math.DG/0102142 | DOI | MR | Zbl

[11] Fu J., Zhou X., Twistor geometry of Hermitian surfaces induced by canonical connections, arXiv: 1803.03894

[12] Fu J., Zhou X., Scalar curvatures in almost Hermitian geometry and some applications, arXiv: 1901.10130

[13] Gauduchon P., “La $1$-forme de torsion d'une variété hermitienne compacte”, Math. Ann., 267 (1984), 495–518 | DOI | MR | Zbl

[14] Gauduchon P., “Hermitian connections and Dirac operators”, Boll. Un. Mat. Ital. B, 11 (1997), 257–288 | MR | Zbl

[15] Grama L., Lima K. N. S., “Bifurcation and local rigidity of homogeneous solutions to the Yamabe problem on maximal flag manifolds”, Differential Geom. Appl., 73 (2020), 101684, 41 pp., arXiv: 1911.06094 | DOI | MR | Zbl

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

[17] Ivanov S., Papadopoulos G., “Vanishing theorems and string backgrounds”, Classical Quantum Gravity, 18 (2001), 1089–1110, arXiv: math.DG/0010038 | DOI | MR | Zbl

[18] Lejmi M., Upmeier M., “Integrability theorems and conformally constant Chern scalar curvature metrics in almost Hermitian geometry”, Comm. Anal. Geom., 28 (2020), 1603–1645, arXiv: 1703.01323 | DOI | MR | Zbl

[19] Liu K., Yang X., “Ricci curvatures on Hermitian manifolds”, Trans. Amer. Math. Soc., 369 (2017), 5157–5196, arXiv: 1404.2481 | DOI | MR | Zbl

[20] San Martin L. A.B., de Cássia de J. Silva R., “Invariant nearly-Kähler structures”, Geom. Dedicata, 121 (2006), 143–154 | DOI | MR | Zbl

[21] San Martin L. A.B., Negreiros C. J. C., “Invariant almost Hermitian structures on flag manifolds”, Adv. Math., 178 (2003), 277–310 | DOI | MR | Zbl

[22] Tricerri F., Vanhecke L., “Curvature tensors on almost Hermitian manifolds”, Trans. Amer. Math. Soc., 267 (1981), 365–397 | DOI | MR

[23] Wolf J. A., Gray A., “Homogeneous spaces defined by Lie group automorphisms. II”, J. Differential Geometry, 2 (1968), 115–159 | DOI | MR | Zbl